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In other words, the flow of the “Future Person” event goes like this:
First, Shiori and I get married. In this timeline A, Rin (red circle) is eventually born, grows up, and awakens to yuri.
When she becomes a high schooler, Rin travels back to the past and, using the Future Person event as a cover, plots to make the Toka × Mikage pairing happen.

Because of this plan, a change in the timeline occurs, creating Timeline B, in which Rin commits her worst-ever Dark History (purple X). Timeline A disappears (time-ability users can retain the memories of erased timelines).

In the future of Timeline B, Rin—now an adult, married, and a mother—is writhing in agony over the dark past she committed.
However, since she has already jumped to the past once, she cannot travel back again to stop her own actions.
So, she entrusts a letter to her daughter Kaya (green circle)—Rin’s daughter and Shiori’s granddaughter—and sends her on an errand to the past.

Because Shota-kun’s exile to the Amazon and his arrival at a Hoppo tribe village sets up a flag between Rin and a Hoppo tribesman, which leads to Kaya’s birth, she lets Shota-kun’s exile to the Amazon play out without interference.

For Kaya, the Hoppo tribe village—though in a different era—is the familiar homeland of her father.
She can speak the Hoppo language like a native, knows many of the people, and since she has come from the future, she can even “predict” the Hoppo tribe’s future.
With all that, it was easy for her to be accepted by the village.

Kaya quickly retrieves Shota-kun, who was originally supposed to spend several days half-dead from diarrhea before reaching the Hoppo tribe.
She then nurses him back to health early.
As the jaguar that had been attacking the Hoppo tribe would otherwise continue to trouble the village for years, she takes the opportunity to have him eliminate it.

Then, riding along with Shota’s rescue, she travels to Japan.
She delivers the letter from “Future Married Woman Rin” to me, and the three of us—me, Shiori, and Kaya—share an understanding about what Rin is about to do, as well as Kaya’s true identity.

And so begins the Darkest History that will torment Rin for years to come.

There’s no point in stopping Rin before the Darkest History begins.
If she’s accused of something she hasn’t even done yet, she’ll just get annoyed.
Even if she grudgingly abandons her plan once to avoid being scolded, if she hasn’t truly reflected, she’ll just do the same thing all over again.
That’s why it’s necessary to rewind time *after* the Darkest History has already started.

After the event of the Darkest History occurs, Kaya uses her ability to rewind time.
This erases the Darkest History (X), causing Timeline B to disappear and giving rise to Timeline C, where the Darkest History never happened.

Shiori, Rin, and Kaya, being time-ability users, still remember the Darkest History (X) clearly, but it’s erased from the memories of everyone else—so as long as they keep quiet, no one will know.
Originally, the Darkest History (X) would have escalated more and more until it eventually dragged in hundreds of people, ending in a truly terrible mess.
If a disaster affecting hundreds can be turned into a secret memory shared only by three people, then the time alteration is certainly worth it.

Incidentally, Kaya’s rewind ability can turn back a maximum of just under 40 minutes, and this doesn’t count as time travel.
If time travel is like instantaneously jumping back into the past, Kaya’s rewind is more like sprinting backwards at full speed, desperately running her way into the past.
Even if she can’t return decades like with true time travel, 40 minutes is more than enough.

After that, Kaya returns the young Rin to her own time, leaving it to the future Shiori—who has been waiting for her—to deliver some strict punishment and education.

Kaya herself returns to her mother Rin in her own time. With that, everything is settled back into its proper place.

What exactly was this “Darkest History”?
What did Rin actually do?
I have no idea.
It wasn’t written in the letter.

The only thing it did say was that the Sago family’s household rule was never to go into the past and stir it up.
Apparently, children born between Espers inherit the same type of abilities as their parents, so in the future the Sago family has become a bloodline of time-users. Perhaps the reason telekinesis isn’t inherited is because of its peculiarity as the “origin” of all abilities.

As for why Kaya tied Rin up and disappeared with her, Shiori gave an explanation that—while leaving out the contents of the Darkest History and anything to do with our little staged crisis—was close enough to the truth to satisfy everyone.
Everyone accepted that explanation, and we disbanded.
After that, Shiori and I quietly called out Baba who’d been handling all the behind-the-scenes setup and adjustments related to Tsukuyomi, and the three of us—together again after a long time—enjoyed a celebration party for our successful event, lasting until dawn.