That's the problem with time travel, it's never really explained. The best we can gather is what James Cameron hints at throughout the 1st 2 movies. "There's no fate but what we make for ourselves". I think that statement can be interpreted as a metaphor for time travel as well. I think what happens is, once you time travel to the past, the future just doesn't exist for the individual who jumped.
The parallel times are just speculatory to reflect possible outcomes. For example, as soon as Kyle Reese goes back, does John Connor change immediately? Likely not. That timeline continues on the way it always had.
Changing the past doesn't affect the "future", but the future of the present timeline. Otherwise, John Connor would've dropped dead as soon as Kyle Reese left because Kyle stopped the "future" John from ever being born the instant he left 2029.
So why does Skynet continue to send terminators to the past, if the future Skynet wouldn't be affected since it exists in that time?
It's just a big convoluted mess when time travel is part of the plot.