Freed from the mechanical arguments, the movie does what it wants with time travel. Mainly, because it is far more concerned with the philosophical ramifications. It's really asking the question that if you could go back in time and murder Hitler as a child, would you? Would that be ethical?
The movie argues that no, it is not. Because that child is a different person than the monster he will become.
I enjoyed Looper, but it doesn't take anything seriously and handles the philosophical shite very badly. Do they know how time travel works? No, but one thing I'm pretty certain about is that it wouldn't work in contradictory ways that conveniently match what a director wants at any point in time. The rules should be consistent and they are not in extremely blatant ways.
The movie doesn't touch on whether you should kill Hitler as a child. It could have been. For whatever random reason they had for the telekinesis in the first place, given the kid's ability, he could have grown up into a walking Death Star who did really bad things later in life.
All he really did that we know of is that he had paid assassins killed and during the process his henchmen accidentally killed old Joe's wife as collateral damage. He, the Rainmaker, was a man seeking vigilante justice, not a genocidal maniac seeking world domination. Old Joe, the former assassin, was trying to save his innocent wife and his own skin. Asking whether the child should die in this example is not a complex philosophical question. As I said, badly done.