From chapter 920 we learned that Lady Kozuki Toki has the "time-time abiltiy". Seeing that she knew the naming convention for devil fruits, in which you say the japanese name twice which then follows by "no mi", as in Gomu Gom No mi or Ope Ope No mi, etc., then she clearly refers to her devil fruit power in this panel with the typical devil fruit nomenclature "time-time". Then why is it that Kinnemon and Kanjuro hasn't any type of knowledge or clue at all of devil fruits, attributing their powers instead to ninjitsu or "magic". We've now seen a range of different devil fruit powers in Wano yet Shinobu again emphasises the fact that the concept of devil fruits are not heard of among the wanoese as she, again, referred to her ability as a "demonic art power". To me it's strange that if Toki in fact knew that these powers originated from devil fruits that she did not reveal this fact to anyone, let alone Kanjuro and Kinnemon who are close friends and allies of Oden. We must seriously be asking ourselves why she would be keeping them in the dark as to what the nature of devil fruits are and what the reasons for this could possibly be, likewise why it is that the Wano people don't know about devil fruits to begin with.
Seeking refuge at the last line of defence: Wano
Toki can travel into the future but not the past, so it's not a farfetch idea that - as people already suspect - she may be from the Void Century and have used her power thus far to travel through time with memories of the Void Century and it's history fresh on her mind. The first time she used her power the Ancient Kingdom may have been on the verge of defeat and so Toki had no other choice but to bring all the secrets and the information of their civilisation with her to the future and pass that on lest she'd remain and be hunted down by the 20 kingdoms as was probably Joyboy and the remaining factions at the very end of the conflict. Hence, Toki is vital in that she is the one responsible for carrying on the legacy if worse comes to worst and the Ancient Kingdom and all it's history is destroyed along with it's advocates like Joyboy and those of his ilk. Maybe she couldn't bring Joyboy with her because he and his followers had unfinished business and duties to fulfill, perhaps because the war was not totally over and that there was a fighting chance left, however Toki had to escape in case they would actually suffer defeat. At the time Wano is an ally of the Ancient Kingdom and so Joyboy figures it's best for her to travel some specific amount of time into the future in Wano where he must've reckoned it's the safest place for her to journey, perhaps because Wano was the last line of defence and refuge from the 20 kingdoms.
A political shift to WG-like tyranny
As of when she arrived in Wano, the future in which she arrived at may have been different from that of the past where Wano was a trusted ally to the Ancient Kingdom. When she arrived Wano's policy of isolation may have been in full force and so she couldn't receive any information from the outside world. Despite the lack of information as to the going-ons in the world, the wanoese inform her about this entity called the World Government which rule much of the outside world. Hence she could possibly put two and two together and realised that the WG consists of the victors of the conflict, i.e. the 20 kingdoms, following the defeat of the Anceint Kingdom.
Naturally then she's hesitant about what to do and who to talk to lest there be actually informants from the World Government secreted in Wano. Naturally she tries to get an idea about how Wano has changed and what relationship and attitude it has to the WG. I'm betting she learned that the ruler at the time has dealings with the WG, trading goods and other necessitites, among which a major export from Wano are seastone weapons sold to the WG as we've learned from Hawkins that seastone tools and items are produced in Wano, and of course we know that the marines have a good amount of seastone weapons and implements in their disposal. She also learns that the current leadership has ousted the Kozuki family from leadership and persecuted them who as a result would've been forced to flee (she reckons they're hiding out at Zou) and as such the current leadership in Wano are on relatively good footing with the WG although to it's people they give appearances of being neutral or totally independent from the outside world.
In this kind of environment she doesn't know who to trust and so as of right now she's working out her bearings. She can obiously not simply leave Wano because of the treacherous weather and the fearsome animals roaming around the country (plus the isolation policy used to enforce control over the popualtion). All she can do is bide her time and wait for the right time and the right people to show up for her to reveal herself.
Why the Wano people are unfamiliar with devil fruits
We can also gather from the fact that as there are no myths or legends about devil fruits in Wano up to this point, we can safely assume that there have never been any knowledge of devil fruits around in Wano whatsoever. Well, actually that's a bit strange given the fact that devil fruits are assumed to have originated from the Ancient Kingdom who were allied with Wano (so we assume). Wano has thus far not been under the heel of the WG as far as we know and so there should be no reason why if there was knowledge back in the days of devil fruits why this knowledge is now totally forgotten or lost, not even preserved in myths or legends.This is why I think that devil fruits may have been weapons used by the 20 kingdoms and somehow Toki ended up with a devil fruit by chance.
Lady Toki "started out early"
As the Void Century stretches back 800 years, she has also likely traveled forward in time on many seperate occasions. Hence, she's obviously not going to get any younger and so I think she "started out early"; she was but a young little girl the first time she used her power to travel forward in time. Toki's job is simply to pass on the legacy and hand down the knowledge of the AK to someone she deems worthy, yet at no point do the necessary prerequisites for this materialise, thus all she's left to do is waiting for the times to and the tides to change something better. She bides her time and travels forward in time many times hoping that each time she finds herself in a new epoch that something new and better has come along.
While waiting for the right people to come along she's going to age just like everyone else, hence she must be very careful not to stay for too long and consequently age within a time period where she fears that her presence won't do much good in terms of advancing her mission (if there are no "like-minded people" to be found that she can entrust her secret to then she can't stay for too long but has to travel forward again an x numer of years hoping that time period holds more promise). Of course multiple journeys into the future in one place must've attracted some suspicion (hehe, this got me thinking of the Back Into the Future franchise) and so people must have noticed something strange about this, hence why there are "rumours" about her being from the past.
Ryuma wasn't the answer
Back in the days when WG forces and other pirates tried to conquer Wano, Ryuuma led a mighty army that managed to counter any attempted inroads into Wano. This bolstered the reputation of Ryuuma as the "god of swords" and gave Wano a fearsome reputation. From here on out Wano became more self-sufficient and cut off all ties with the outside world. Even if Ryuma was a good guy he wouldn't have cared whatever Lady Toki would've told him about the Void Century and Ancient Kingdom because no matter what he isn't going to care about taking up the struggle and try to reenact the ideals and values of the AK of peace and unity among the races and all of that simoly because I don't think Ryuma wouldn't give two shits about any of that as after all the horrors of the conquering hordes he's witnessed he doesn't want to have anything to do with any foreign people. All Ryuma cared about was building an army strong enough to repel any foreigners from ever daring to come to Wano in the first place, to protect Wano from any foreign influence; while the AK worked to unite the races and the people of the world, Ryuma sought to isolate Wano entirely from the rest of the world. This is why I think he also did away with the leadership that were friendly with the WG and replaced these with isolationist politicians. Thus, Toki realised that Ryuma wasn't the answer and so continued with her seemingly never-ending journeying through time.
The Roger Pirates "spreading the good news"
Howerver, scroll forward time 700 something years and now the Kozuki clan has returned and regained power, though the shogun (the father of Oden that we haven't yet seen) is still holding onto the policy of isolation and self-sufficiency that was set by Ryumma. Despite this Toko now realises that the time may be right to try to ingratiate herself with the Kozukis seeing that these are "her people" afterall with lineage stretching back to the Void Century. She marries Oden and has two children with him. She still can't reveal too much, though, fearing that that information could blow her cover (WG may still have double agents planted in Wano she suspects) so she patiently waits. Oden sets sail with the Roger pirates and he later returns bringing the good news of the "dawn": the history of the Void Century uncovered by the Roger Pirates. Upon this reveal he also explains to her about devil fruit powers,and from this she learns about the typical naming-scheme and nomenclature of devil frutis (hence why she called it "time-time ability" and not simply "time travel ability" or something along those lines).
This I think must've gotten her a little riled up from joy about the fact that the Roger Pirates are ushering in a new era that may lead to future generations discovering the true nature of the Void Century, and so now she feels more certain than ever to reveal everything about herself to Oden and about her past, spilling the beans on all the juicy information about the Void Centuty and Ancient Kingdom on top of that that he already discovered from travelling with the Roger Pirates. However, Toki is not really on her guard as I think someone overhears this conversation: that someone is a double agent working for Kaido.
Kaido looking for some long-forgotten "information"
That is why Kaido attacked Oden. I believe that Kaido was in fact not looking for Oden but was looking for Toki that day when he attacked and overthrew the kozukis; which is why Kinnemon said that Kaido was looking for (in quotation marks) "information" (a low key hint from Oda that he was looking for something else than what Kinemom is portraying it like).
Kaido proceeds to attack Wano, finds Oden and demand that he tells him where his wife is. Oden subsequently refuses and in anger Kaido kills Oden. If he really wanted to know something about Raftel it would've made more sense to keep him alive and extort the information out of him, threatening with murdering his family and so on like he probably did with Kamawatsu. However, Oden is just some guy who knows what the One Piece is, but Kaido has probably figured out that the One Piece is not the end-all-be-all and that there's something more that only someone with direct ancestry from the actual Void Century or Ancient Kingdom would know and be able to tell him. There is no reason why Kaido would kill Oden if he was the target all along. No, Oden wasn't the target; Toki was the real target. The "information" was not information he could get from Oden but information he could get from Toki.
Betting on the new dawn
Toki hid out in the castle and decided to travel forward in time with her two children. She deliberately set the castle on fire to prevent the enemy from reaching her. However, the nine scabbards managed to reach the castle before she set off and then we have Kinnemon talking about his wish to fullfill Oden's dream of opening up the borders". Upon seeing this Toki smiles, somehow this reminds her of joyboy's will most likely.
She could've decide to spirit herself away with nothing but herself and her kids (sorry but the time-continuum can't be too cramped up with too many people). However, I think she decides to make an ultimate "bet" (a running theme in the the series) that these are the people that are going to continue the legacy of the Ancient Kingdom; this is what she's been waiting for for all these hundreds of years. She ultimately sacrifices her life for the nine scabbards to live on. Her mission is now complete and the new dawn is finally in sight.
Lady Toki got her hands on the time-time fruit by accident because devil fruits were originally weapons used by the 20 kingdoms. She was but a young girl when she journeyed in time to Wano and found herself in a situation she could not recognise where the Kozuki clan had been driven out and where new political alignments made it impossible for her to out herself. Hence, all she could do was biding her time. Ryumma was certainly hostile towards the WG but I believe was equally hostile to making any attempts to change the world order or forging alliances with other people, being content instead to keep Wano secluded and self-contained part of the world, unconcerned about whatever was going on outside its borders. Thus, Ryumma wasn't the answer either. The Roger Pirates were the right ones, though, and this made Toko at last out herself to Oden. Someone working for Kaido overhears this conversation and so now Kaido knows about the Void Century and about the One Piece. However, he isn't interested in the One Piece but he is interested in something particular that Lady Toki knows about, some particular piece of "information" she is privy to. Lady Toki is about to hit some alternate spacetime-continuum with her kids just as the nine scabbards arrive at the castle. Kinemom expresses the wishes of Oden but also (unbeknownst to him perhaps) he also expresses kind of the the ideals of the Ancient Kingdom and upon witnessing this Lady Toki makes her "bet" and sacrifices her life so that they can live on and carry on the legacy and the will of the Ancient Kingdom.
Thank you so much for reading and have a nice day!
Speculation The history of Lady Toki and Wano post Void Century; Kaido targeted Toki, not Oden.
How Lady Toki ended up journeying through time in Wano - and how Kaido figured out her history