I guess the mechanism is just a constraint on the possible solutions for the scenario. As an analogy imagine holding a rope in your hand and wiggling it up and down, this way you can make waves of more or less any wavelength travel along the rope. Now fix the far end of the rope somewhere or close it into a loop and you will no longer be able to make waves of arbitrary wavelength but only integer or half-integer fractions of the rope length.

In case of the loop the two ends of the rope are now identified and therefore must have the some displacement at all times which you only get if the wavelength is an integer fraction of the rope length. I haven't thought about this in much detail but I would guess that if you wiggle the rope at one point the wave now goes both ways around the loop and interferes with itself. Similarly for the rope attached at the far end the wave will be reflected and interfere with itself. In the end the result of the interference is probably strong damping of all wavelengths that do not have a suitable wavelength.

On the next level down you could than analysis this in terms of the atoms and the electromagnetic forces between them which in combination give rise to the macroscopic behavior of the rope. And as I said, I guess time travel self correction would be essentially the same thing, some kind of interference effect disallowing certain solutions. Just like in the loop example where you can not wiggle the rope in a way that the two ends of the rope have different displacements, i.e. you can not go back in time to kill your grandfather and have this prevent you from doing so. There is a consistency constraint by the rope being a loop and the rope not allowing discontinuities in it.

How this would work out in a complex system that involves the real world and people trying to kill other people is probably really far beyond human ability to figure out. Maybe just one neuron in you brain would not fire and prevent you from pulling the trigger. Maybe aliens would capture you on the way to your grandfather. Maybe something would get into the way of the bullet and capture or deflect it. Impossible to say.