My usual take is that if a battle was close enough for the reinforcements to tip it in the favor of one side, it's not an unreasonable thing. IOW: not really, no, considering that the 9k were apparently already holding their own against the 25k.
That's the sort of situation where there's got to be something else going on: the 25k already had low morale, the 9k had markedly higher tech/were defending on good terrain/had an excellent leader, &c. Reinforcements don't turn a definite loss into a definite win (unless it's something major like a 20k stack rolling up near the end of a 25k vs 50k or whatever).
Be careful with autonomous rebel suppression. An army will automatically attack rebels sieging a mountain province across a river, which is a major penalty.
If rebels siege a province adjacent to a fort it won't give the province any negative modifiers (like 10 years of separatism in this case). Pick your battles wisely.
True--but again, that's why I noted that it's situational. If terrain penalties are enough to make your forces lose, your stacks aren't beefy or numerous enough to just leave it on by default. If any rebel stack is going to have multiple 20-30k stacks attacking it at the same time, on the other hand...
That said, you can also manage initial movements manually and then turn it on after your first or second victory, since the AI is pretty much always more efficient than you are at chasing down retreating losers.