Nope, that's what I was saying. It doesn't change time it starts a new time line independent from the last. That way you don't have the whole Back to the Future thing where Marty would disappear from the photograph because he did something in the past. The Terminator would still have come back but on the new time line he may not necessarily still exist in the future in his same exact form... but that doesn't matter because he came from a separate time line thus having no effect on the new one.
The main mistake I made was here:
"Kyle tells Sarah about judgement day he is referring to his own time line and not the parent time line in which it may not have occurred for many more years."
Which does necessitate a pre-determined future and doesn't really make any sense.
Here is an updated diagram that sucks less (timetravels in red):
