The way I see it, there's two dimensions of time: one being linear time within the TVA, and the other being the time that everything else experiences including us, which branches. The TVA therefore doesn't branch, because it experiences a different axis of time. It's self-consistent in that sense where the TVA's time works the same always, and the time of everything else works the same always (if you ignore Cap), at least for now.
to be fair, from a Doylist point of view without that there is no show to be had lol. TVA becomes an entirely useless organisation unless it can work from beyond the multiverse, and the only way it can work from beyond the multiverse yet have change in it is if there is a dimension of time in the TVA.