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This is fundamentally a variation on the question of a Temporal Paradox, also known as a Grandfather Paradox ("You go back in time and kill your grandfather. What happens?"). Although no killing happens in this variation, the basic idea is the same: Information is transmitted to the past from the future, but results in a situation where it cannot be transmitted in the first place.
Accordingly, there are several hypotheses to cover this. This isn't even all of them:
I think the idea of parallel universes solves time travel paradoxes in a pretty clean way.
Except for the fact it makes every decision, every moment of tension and every event that occurs irrelevant, because an infinite number of universe exist in which the events occurred and in which they didn't occur.
Even knowing that everything happens every way in some other branch of the wave function (other universes) doesn't really affect our own little section of it. There's no communications or travel, so other universes if they exist have the same meaning to us as if they don't. Except in time travel stories like this.
Besides, the same "irrelevance" of decisions and events comes free with even one single universe given that it's deterministic - as physics seems to be. (Yeah there's quantum randomness, but random doesn't help either)
That said I still believe in free will and the importance of decisions. I just think it has to be defined so weakly that it still works in a deterministic universe. (So I have free will, but so do dice and pocket calculators.)
I'm not talking about about the possibility of real infinite dimensions. I'm talking about sci fi, and stories, which is the context of the OPs question.
In a "real" scenario, the experience that matters is the one I'm having, not the one other versions of me might be having.
But in a story, there is no "true" timeline, or a more "real" timeline. They're all being retold to us indirectly, and the choice of the version of the person retelling those experiences is arbitrary by the author. It doesn't matter what perspective the author chooses, because every other outcome also happened, the author just didn't tell us those stories.
I'd say that the one that's written is the 'true' timeline in the story the same way that the reality we experience is the only one that matters.
The reality I experience is the only one that matters to me. To an outside observer, all of them are as equally real and there is no true timeline.
In a story, there is no real, there is only outside observers...