Im not exactly sure if they are traveling around helping people in parallel universes, but i think they are there *trying* to help Booker fix his mistake because in a way, it is thier fault too. Booker has tried this mission many times but keeps failing. if you notice early on in the game, you can see on the chalkboard Mr.Lutece has strapped to his back, that Booker has tried over and over and over again by seeing how many times he had picked the number.
The Lutece twins have seen Booker try and fail so many times, that they are numb to it, and are basicly guiding him over and over to the same outcome. (which explains why they are always acting goofy as if all the shock and urgency has worn off and they are just going through the motions) so which leads me to believe they are just trying to help Booker and probably no one else.