As stated above, AST manipulate fate by drawing on celestial Aether. This allows them to manipulate space, time and probability. However I don't think they can simply dictate those things.

Why doesn't it get abused? Two reasons I suspect. First it sounds like that it is very hard magic to manipulate and secondly it sounds like its very powerful magic to cast and as such the caster is limited in what they can do by the amount of Aether they can muster. Its the same reason a BLM can't level the twelveswood with a single spell. Sure it might be possible but in most cases it's far beyond the capacity of the casters without a great deal of preparation and setup.

The ability to stop time was considered a rumor among most ASTs.