If DTI has arrest powers,it would have an almost 'precrime' M.O: arresting or detaining individuals who technically are not guilty of a crime in the case of future timeline violations.
And how can they determine a timeline violation has occurred?
It wasn't DTI but it did seem that by the 29th century Starfleet could arrest/detain its personnel before they committed a crime. Been an age since I've seen the episode but that was the case with Braxton if I'm recalling the episode correctly. He was arrested before he would have commited the crimes of using time travel to blow up Voyager
...though given some of the fan base around here they probably would have given him a medal and promoted him to Chief Timey-wimey guy.
Got to wonder about those two DTI guys in TaT given they failed to notice the fact that DS9 was crawling with a previously extinct species.