Time has two dimensions
I think this is the basic assumption that needs to be made, in order to for full sense to be made out of the awesome story that is Rant.
There are no alternate or parallel universes. Just the one universe, with the regular three dimensions of space, but two of time.
Time having two dimensions simply means that going back in time and changing things, creates a new reality, from the old one, which becomes, to everyone who exists in the new reality, what appears to be the only reality there ever was. At least until the next whatever change gets made.
For example; A man named Charles Casey goes back in time and impregnates his own grandmother with a new version of his own mother who goes on to give birth to a new version of himself.
In this new reality, the new Charles Casey who goes back in time to impregnate his own grandmother is a different man to the man who originally went back in time and impregnated his own grandmother. That Charles Casey, along with the old reality he came from, no longer exists. He and it were just the precurser/cause for the new one. He would look different, have different memories as a result of experiencing a different reality, etc.
But possibly only slightly different. That he is still there traveling back in time and impregnating his own grandmother, means that there are still common elements, a kind of 'course correction' must be at work. So that in such a universe the reality isn't so fragile that it gets completely changed by the flap of a butterfly's wings, but "more like a chain link fence you can't hardly fuck up."
Especially if the current reality is something that has already been set up by other time travelers who have a vested interest in keeping things as they are...