The classic "butterfly effect" in time travel is when a minor change in the past causes major changes in the present/future. A traveller goes to the era of the dinosaurs, steps on an insect, and human civilization is radically different or doesn't exist at all when he goes back. A hilarious example occurs in "Time and Punishment", a story in The Simpsons Treehouse of Horror V in which Homer turns a toaster into a time machine.
This contrasts with what might be called the "killing Hitler in 1918" effect, where a time traveller makes a deliberate, major change in order to alter the course of history. The plots of the films are all about Skynet trying to kill its mortal enemy, John Connor, before he can destroy Skynet.
The characters in the films steal things, wreck cars, burn down buildings, and kill or injure dozens of innocent bystanders. This should be more than enough to invoke a butterfly effect, if one exists, but we don't see it happen.
For example, in The Terminator Kyle Reese seems to be invulnerable to the butterfly effect. He led a very dangerous life before travelling back in time to protect Sarah, first in Skynet's death camps and later as a fighter for the resistance:
REESE: Some of us were kept alive... to work... loading bodies. The
disposal units ran night and day. We were that close to going out
forever. But there was one man who taught us to fight, to storm the
wire of the camps, to smash those metal mother****ers into junk.
If the butterfly effect applies, it could very easily result in Reese's death before he goes back in time. But if that happened,
he would be unable to father John Connor with Sarah
and a major paradox would result. So we can conclude the butterfly effect does not apply -- or at the very least, time travellers are somehow protected from its influence.