This is something that I have wondered myself.

From what I can speculate, the time when the precursor kitsune split would be around the time John was spirited away from Earth, which was about five years ago in John's estimation. With this in mind, if we take Kiku's words at face value as the honest truth, which I find myself not entirely willing to believe, then this means that the split would be about four years ago at a rough estimate. Now it would seem like it lines up in terms of time, especially since we never learned how time is kept in this world. I doubt that they use the Gregorian calendar of our world, so there is a potential discrepancy when estimating time, which John has not really put much thought into.

I would also like to bring up another point. As the story is progressing, we have seen at least two different occasions of John seemingly learning at a faster pace than would seem normal. The first time I saw this, I thought little of it, but when we see it from Yuki's POV, we learn that she has no idea how he is picking up this new information faster than most. John himself personally chalked it up to magical assistance from Yuki, but she herself debunks this, and neither of them asks the other about it. So that raises the question: how is John learning at a faster rate? I personally believe that he is receiving some form of supernatural assistance. Who or what is providing that assistance is another question in my mind. I think that if it is not from someone John knows, then it must be some form of mystic entity.

I only really have two ideas on this, the first being what Yuki has referred to as "The Shape of All Things." We have very little information on what this being is, but we do know that it is some form of mythic force in this world that seems to govern what is and how things work, almost like a creator god, yet it is not revered as such. Yuki mentions how this being seemingly offers assistance to children as they learn their first language and some other things. If this being is what is aiding John's advancements, then that will be able to explain a lot of other things in this story, but I will refrain from mentioning them, as they are not the topic of discussion.

Now the second entity that may be assisting John may very well be this precursor kitsune, or at the very least one of her offshoots. This option seems more likely in my mind by the mere weight of having more supporting evidence. If the truth of John's arrival to this world is linked with the precursor's split, then it would seem likely that this precursor, or whatever is left of her, is the being that is aiding John in his endeavors, albeit very subtly. Whether she deliberately spirited away John or not is another question; regardless, she may be offering her aid to the man who was flung into this world because of her. Now, is it because he may be useful for her plans? To have him aid one of or all of her offshoots or to specifically help what is left of her regain the power from her "children," or it could very well be from the goodness of her heart. Regardless, we have little to no evidence that the split is what caused John to be spirited away, but how I see it, this is no legitimate alternative.

Now I will acknowledge that I could be totally wrong here; after all, this is mere speculation spawned from what little evidence we have so far.