The thing is, you don't really have to explain that, exactly because we don't know what the "rules" of time-travel are, IF it were even possible. We talk about "grandfather paradoxes" and "ontological paradox" in sci-fi, and speculate about what would happen in "real life" if some of these things happened, but the paradox might be completely irrelevant for all we know.

Anyway, for my money, this issue falls well into the "willful suspension of disbelief" category - and didn't affect my appreciation of the movie at all.

I mean, yeah, it was billed as a "scientifically accurate' movie, but it's still science fiction at the end of the day, with the emphasis on "fiction".