I've been watching the 12 Monkeys TV show, which is based off of the 1996 movie of the same name. Time travel is a major part of that movie, and I have found [a thorough fan explanation][1]a thorough fan explanation for how it works. Essentially, each major change to the timeline results in a new timeline being created, which seems to me to overwrite the previous timeline.
However, things don't seem as simple in the 12 Monkeys TV show. In the first episode, Cole demonstrates the effects of temporal paradoxes by scratching Frost's watch and showing that the scratch has instantly appeared on the same watch that he brought back from 2043. Additionally, Dr. Goines says that he has already met Cole, yet it is unclear to me if there are multiple timelines as there was in the movie.
So does time travel in the 12 Monkeys TV show work differently than in the movie? [1]: http://www.mjyoung.net/time/monkeys.html