F=ma, so -F = -m * a. If mass becomes negative, then so does force. That's negative force. In simple terms, negative force is force in the opposite direction. That's why events would occur in the opposite direction.
Think about it like this: Ball A is rolled over a table, hitting Ball B. Afterwards, the mass of everything becomes negative. Now, Ball B has negative force, sending it in the direction that it was leaving. The ball collides with Ball A, and Ball A is returned to its starting point. The instance at the start of the scenario has been restored--thus, Ball A and B 'rewinded' into the past.
We don't usually consider 'changing' positive mass to negative, so I can understand the confusion. Such an event isn't commonly pondered about. Correct me if I'm still wrong about it.
In reference to the conjecture about gravity, our current understanding of it is incomplete. More pieces are needed. The idea mentioned is meant as a proposal to fill these missing pieces, without going against our current experiments.
The question is whether it does this. There's certainly mathematical work that has to be done to see how it holds up--for now we'll look into proof of concept, though, since this is speculation. Might it work with what we know?
I believe it may--it explains things in more depth than the General Theory of Relativity by itself, without removing its idea. The interactions of negative mass with positive mass would cause the curvature of space-time. Also, the more positive mass, the more negative mass would be attracted. In turn, groups of positive mass would cling to the negative, coming closer to each other in the process. In this way, attraction would be increased between positive masses, indirectly due to their mass. This makes the relationship between positive mass and gravity less precise but present, explaining the problems Dark Matter was meant to fix. A lot of math will need to be looked at for this.
In a more abstract sense, understanding gravity as 'opposites attracting' would fortify its relations to electromagnetism, which is an important problem in Physics. Gravity and magnetism are similar, so its worth considering whether their functions hold similarities, as well. I'd like to here any more ideas, really.
As for the last part of your post, you're completely right. I should have said that 'rewinding' is being described through the behavior of negative mass, instead of negative mass itself.