A.) There is not chance that this movie is intended to be in some kind of alternate time line.
B.) As to being 'fast enough' to fix an alteration in the time line, the only way you could do that is to stop the person from jumping back in time. The very second they make their jump back, any action they take back in the past, even if it takes years or decades for them to achieve their goal, has already occurred in you time frame. If you plan to chase them back in time and you make your jump even a fraction of a nano second after they do, you are too late.