simple answer is that small edits in the timeline didn't effect anything "major"
Less simple answer (beware of timey-wimey stuff):
Consider this.
<PERSON> was sent back in time because the first Terminator was sent back in time. The first Terminator was sent back in time because the resistance was winning, and <PERSON> wanted to kill <PERSON> before he could become a problem (by killing his mother pre-conception). This is impossible because to do so would invalidate the reason to send the Terminator back in the first place.
Now, <PERSON> became <PERSON>'s Father. Had he not been sent back, <PERSON> would never exist, the machines would not have a reason to send the Terminator back, and stuff would break.
Here's the thing. You ask about multiple futures with a single timeline, but you don't specify WHICH timeline. Each individual has different timelines in relation to the other characters. <PERSON>'s timeline involves him going back in time, fathering <PERSON>, and dying. However, that's HIS timeline. <PERSON>'s timeline has <PERSON> eventually being born, then sent back in time. When <PERSON> gets to the past, he creates <PERSON>. The same <PERSON> that sent him back, mind you.
Now the complicated part. the major events, the pieces that influenced the time travel, the core reasons for doing so never changed. skynet was created. The resistance is born. <PERSON> and the resistance kick ass. The Terminator is sent back in time. <PERSON> follows him. all that still happens in the "changed" futures from the later films. 837
The details that do change are things like the date of Judgement Day. Regardless of when the war starts, the end result is the same. Thus, the start of the war doesn't matter. It is in something like a temporal flux. Because the exact date it begins is not important to the time travel plots, it can be altered slightly. Causality will not allow the complete prevention of the war. If the war never begins, then the Terminator isn't sent back, <PERSON> isn't sent back, <PERSON> isn't born, and there is nothing to stop the war. BUT, because <PERSON> (and in T2 <PERSON>) are sent back and tell <PERSON> about the future, her actions are able to influence events in flux. She can't stop them completely, but they can be changed. Perhaps over the many loops the changes were incremental, but by the time T3 comes around, the changes have pushed the beginning of the war back a good ways.
The major issue at hand is that there are two separate veins of time-travel/causality theories. One says that a new timeline branches off when one goes back in time (not "going back in time" as much as simply going to a different alternate universe/timeline where conditions are identical to how things were at the target point. See: Dragon Ball Z). The second says that causality is absolute, and there is a single timeline. any changes made to the past have already occurred, and thus are not "changes". They're simply events on the (immutable) timeline. Once something has been experienced, it is frozen and will always happen.
The terminator Universe mixes both theories to an extent. They generally follow absolute causality, but allow for some changes. Thus, it is hard to reconcile these things.
tl;dr is that the "changes" are minor enough to not actually effect anything important temporally speaking, though should not strictly have been possible. 55