On Thomas Granger's coma, Shane Carruth (Primer writer and director, and also the actor who played Aaron) himself says that it is due to a paradox. Quoting Carruth in an interview, he also uses the terms "feedback loop" and "recursion" to describe what happened to Granger (emphasis mine):
Can you elaborate on the concept of recursion in terms of time-travel paradoxes?
Shane Carruth: I have a degree in math and my favorite subject was non-linear dynamics. You have an equation y = x, and you take that answer and feed it right back in for x, and you chart this and sometimes you get fractals and sometimes you get orderly systems. The idea of recursion and whatever it leads to—that informed a lot of the story, the idea of creating a feedback loop. This isn’t really addressed in the film, but the reason Granger is unconscious is because he’s suffering from recursion. What I think happened is that Abe told Granger about the machine. This man who’s been told by Abe about the machine uses the machine to come back and somehow has an interaction with Abe so that now Abe probably won’t tell him about the machine and yet he still finds himself there. Without coming out and saying it, the film is built on the idea that these paradoxes are a way to understand things. The universe is not going to explode or break down if you create a paradox. Whatever’s going to break is probably going to be you.
Source: "A Primer Primer", The Village Voice
Aaron-2 (Narrator): [...] what the world remembers, the actuality, the last revision is what counts, apparently.
Based on the above dialogue, while we see multiple timelines in the film, only the last revision "counts." Only the last revision will affect the universe.
So even if different timelines are apparently shown in the film, some of those scenes are just earlier iterations/loops. And since those were from an earlier iteration, those iterations are modifiable.
Aaron hints to this in his dialog:
The worst thing in the world is to know that the moment you are experiencing has already been defined, that this is the second or third time through, or whatever.
And do you ever feel like... maybe things aren't right, like maybe your life is in disarray or just not what you would like and you start to wonder what caused this. How did things get like this?
What if you knew for sure this is not the way things are supposed to be?
We later see characters go back in time to attempt to "right" certain things, even taking more than two loops to do so.
Throughout the movie, time-travelling versions of Aaron and Abe drug their doubles, preventing them from getting into the boxes and time travelling themselves. This doesn't seem to affect the time-travelling Aarons/Abes though, so why would a time-travelling Granger be affected?
I think this is because the paradox is unresolved in the loop/iteration where we see Thomas Granger-2 back in time (~2:00 AM Friday). Aaron-3 (white jumper Aaron and [who I believe to be] the Aaron we see in most of the film) hasn't resolved the situation at this point. We later see Aaron-3 resolve the situation at Robert's birthday party (Monday) involving Rachel and her ex-boyfriend. We don't know how many loops it took Aaron-3 to resolve it.
Also, we didn't see if the drugged Aaron-1 and Abe-1 were prevented from time-traveling at all. Aaron-3 thinks that they will eventually build their own time machines as per his dialogue to Abe-2: "They'll be building their own boxes in another day. And yours already knows what they've built."
Aaron-2: So how many times did it take Aaron as he cycled through the same conversations lip-synching trivia over and over? How many times would it take before he got it right? Three? Four? Twenty?
Aaron-2 narrates the above during the scene where Aaron-3 and Abe-2 are at Robert's birthday party (Monday). Aaron-3 resolves the situation in that scene, by stopping the gunman, getting him arrested and jailed. Since that is the last revision shown, that is what "counts" in the timeline and the paradox is now apparently resolved (possibly preventing Thomas Granger from coming back in time [the Friday of that iteration wasn't shown so we can't be sure]), since Aaron-3 was now planning to leave the country the next day (Tuesday), instead of going back in time again, and doing another loop to try and resolve the situation.
Aren't the timelines independent? Any action that a time traveller performs that would prevent his/her double from time travelling shouldn't matter, because the time traveller's native timeline is independent from the current timeline that he/she finds him/herself in.
As per the above, there is actually only one timeline as only the last revision "counts." The other timelines shown are just earlier iterations, and as we see in the film, can be changed in a later iteration.
If a time traveler would prevent their double from time-traveling, this will result in clones. e.g., Abe-2 drugging Abe-1, preventing the latter from time-traveling that day. And also when Aaron-2 (hooded Aaron) and Aaron-3 (white jumper Aaron) fought, this ended up with Aaron-2 leaving town and not going back to a time machine to do another loop, as he would have done in an earlier iteration. With Aaron-1 drugged, and Aaron-2 leaving town, this made three separate Aarons (that we, the audience know of) at the end of the film.