One point that came up was the whole 'Kill the baby in its crib' method. But the method of time travel is also to our discretion. It could be that at the point when a truly evil person commits to acts of atrocity, it ripples through all known universes, and breaches time and space. This in turn would allow Time Assassins to step into these breaches using technology from their time period to the point where the target is of age and status (Hitler would be Hitler as we know him, and it prevents you from killing the child in the crib).
The Rifts themselves would be opened from a piece of technology on the assassin, but the destination would always be a tad hap hazardous, a little bit like the TV Series Sliders; you can detect an opening and activate it, at which point you’d step through it and end up in X time zone.
Of course, this brings up the question of how they get their orders. An agency that can have time travel would possibly have a means of sending things back into the past to a specific point in time from their command centre in their present time period. Perhaps, the Assassins aren’t the only agents that travel back in time, which means that other, more intelligence based operatives are going back in time as well. Experts in their destination time period, these operatives blend in with a frightening level of accuracy and a strong low profile, passing unnoticed through the remainder of their time. The Agency would give these operatives lists of intended targets and the Assassins would be given the means to seek out these lists and check which targets are present in their current time period. Someone who jumps back in time and finds themselves in 1930’s America could check the newspapers daily until they discover the clue of their intended target and then act upon those clues. The Operatives that went back previous to them would be able to infiltrate or even influence period media, allowing them to insert the messages. A common cipher would be present.
This brings up the issue of what happens if two Assassins end up in the same time period, or even how the targets would end up on the list of the Operatives in the future if they were in fact dead before they were able to commit the atrocities, but then again, that would send us back to square 1, where we’d be discussing methods on how to travel and OMG MY BRAIN!