the rules of time travels are not that hard to figure out...
Ok i'll try to summerize. Time is non linear, if you have the ability to traverse it, it is very fluid and shapes itself.
If you go backwards and make a catastrophic change you can alter the timeline seriously...
There are things like a time loop like bill and ted's excellent adventure and the terminator where it's supposed to end in the future tense if you send something to the past from the future, the events play out like they're supposed to, so that way when that character gets to that moment in time that started the loop he has to complete it.
Continuum had a fracturing of time where the future alec sadler sent his past self a message and sent the terrorists back in time to change the past, and even after everything where time split into another timeline they corrected it...
I hope that helps if anyone can add to it please do...
PS edited to add:
there's another movie that came out called the time machine which had an interesting premise of time travel / vs fate which was crazy because the main character was in love with his girl but she died and he completed the time machine to go backwards and try to save her but no matter what he did she ended up dying... In that case it could be Fate asserting balance to the timeline itself. and the ironic thing is the time machine broke so he only went forward into the future he couldnt go backwards anymore...