Mmm... well, maybe I'm in an error... and after all this is a theory. But I think this work some sort of this way.
Life (yeah, it exist) is about possibilities, which means that our actions tend to change in small or big scale the way the world continue to exist, his shape, in simple words, but we cannot backtrack them.
So time travel is still into that kind of possibilities only that it works in a different sense. Think about time travelling just in the way that a writer look upon a book. When something is wrote you can change it from the outside of the written world, but from the inside it's seen as a unchangeable reality. (A bit of Deux ex machina if you ask me.... or in this particular case "Entity ex machina")
Time traveling then alows you to rewrite the temporal equations, because as we all know there are a lot of ways to reach a result, be it the same or different, sort of what happens in chrono cross.
My point here, to make this short and simple is that perhaps we are thinking that leaving a place changes ALL the possible futures... while in truth, things only change if they are o aren't realized.
If we see it this way, the last theory makes pretty much sense. Because Ayla travelled BEFORE having kids.. so the story didn't change... or we can see it in the other way that no matter when an event happens it's his fullfilling what matters. (This last point allows the changes made because that lapsus of time possible, but still mantain the great design unchanged).
Seeing it this way, and setting something as an example, we can take the bad end. If our heroes died before the defeat of Lavos, then all the options to change the future would had been futile, cuz they dissapeared in the stream of time. But this didn't mean that they never existed... they simple dissapeared from their timelines, probably alterating the future with unexpected consequences. (Like Guardia waging a war to find princess Marle... or the events of Chrono Cross being unable to happen, in the way they happen)
Well, that is. Sorry for pointing the obvious... but well, hope it serve in some way.
That's it. Bye
