There are a few different ways time travel can work if you assume a branching timeline model where each trip back takes you to (or creates) a new timeline. The first, perhaps simplest model is the one that says "when you go back to a given date, you arrive in a timeline that was identical to the one you just came from up until the date of your arrival, after which it can diverge". However, a little thought shows that this model probably doesn't work for T1 or T2 (since this interview with the writers of Genisys seems to imply they do treat T1 as the "original" timeline(s) that areis then altered by the appearance of the T-5000, Skynet's human formthe Skynet-in-human-form who has learned to hop between timelines, while they mostly disregardingdisregard T3 and takingtake their time travel mechanics from T2). Note that in both T1 and T2, the two time travelers seem to arrive at slightly different moments in the past--in T1 Kyle Reese seems to arrive a little bit after the Terminator, and in T2 the T-1000 seems to arrive a little bit after the T-800. But under the branching-timeline theory above, assuming there was some "original" timeline A where neither member of the pair arrived at that date, it seems as though the second time traveler isn't really arriving in a timeline B that was identical to the timeline A they departed from up until the instant of their arrival. Instead, the movies show them arriving in a timeline B where another time traveler has already appeared a few minutes/hours earlier, already causing a bit of divergence from the history of the original timeline A they came from, where no time travelers appeared on that date. So, these movies don't seem to be consistent with this model of time travel.*
There's a second possible branching-timeline model which involves a sequence of different timelines A, B, C etc., where all the time travelers who depart from one timeline will appear at the appointed hour in the next one in the sequence--so for example all the time travelers who depart from any point in history in timeline A will arrive in timeline B, all the time travelers who depart from timeline B will arrive in timeline C, etc. (A model like this is discussed on this page about a time travel roleplaying game, see especially the scenario towards the bottom of the page involving time travelers who want to interact with Hitler and Marx and the diagram of the different timelines created.) This type of model has some strange consequences. For example, suppose on May 2 2150 of timeline A, I decide to travel back one day to May 1 2150. Then 3000 years later in the 5150 of timeline A, some other time traveler decides to go back 65 million years ago and stop the asteroid that caused the extinction of the dinosaurs. In this case, we will both arrive in the same timeline B, meaning that even though I only intended to travel back one day, I'll find myself in a world where the dinosaurs never went extinct and no humans (aside from fellow time travelers) exist! This second type of model probably wouldn't work very well for science fiction stories since time travelers would almost never end up in anything recognizable as their own past (unless only a few trips back in time are made in the entire history of the universe), but you could make it a little more usable by saying that two time travelers from timeline A can only end up in the same timeline B under certain circumstances, like if only a small time elapsed between the moments they each departed from timeline A, and that otherwise they would end up in different timelines as in the first model.