You seem to be requiring the movie to follow Back to the Future/Looper rules, where something that happens to your earlier self "ripples out" to your current self, or you think there has to be some sort of "stable time loop". The exact mechanism of the time travel isn't pinned down, but it's clear that each version of a person is a separate person. One interpretation is that the government has discovered a portal to a parallel universe that is four days behind ours. The Carlin we follow through most of the movie goes to the parallel universe and dies. The Carlin of that universe is still alive. Carlin finding out about portal, etc., are all things that have already happened in the "original" universe (although this doesn't seem to be the original original universe; this universe seems to be interfered with by another universe four days ahead of it, and that one probably was interfered with by another one, and so on), and nothing that happens in the parallel universe affects that. There are various other ways of describing it that are equivalent.