Lets face it. The first thing everyone would do if this got implemented, would be to have Cave-fish-man citizens.
I~t's beginning to look a lot like fishmen, e~verywhere I go.
Now if only we could get cross-breeding rules...
To go back to the serious side of the suggestions, though, I do think that one of the better ways to make the animal-people cultures less of a resource to just be exploited on the assumption that they would of course want to become a part of "superior dwarven culture" (because, really, who WOULDN'T look at the squalid hole your dwarves live in and instantly become green with envy... or is it green from the choking sulfurous gasses from all the magma you pipe over your blasted Hellscape?) would be both the use of a "cultural pride" meter and the pressures they face from external forces. A culture that has faces no military threats and can feed itself well has no need to risk trusting those crazy dwarves and working hard labor in dwarven mines for food they can already get elsewhere. A starving or militarily defeated and demoralized culture, meanwhile, will be willing to make a deal with the Devil, and if they're even more desperate, worse,
players to take a wild shot at survival.
If they become less desperate, they may want to have relations cool somewhat and bargain for better deals for their continued labor or break off. Cultural indoctrination should be a very slow thing unless players use totally brutal methods, such as the infamous
Stolen Children methods of Australia, and so it could create a situation where just plain being nice may not always get you everything you want, but cruelty can have disastrous long-running consequences as well, (provided you can't just genocide them out,) so that skill with negotiation may play a greater role than simple noble intentions or ironfisted power.
To add to this, you could have a degree of difficult-to-control dwarven sympathy/prejudice, where good treatment of natives will lead to some dwarves being angry, and poor treatment of natives, especially ones that are friends to those dwarves, will lead to other dwarves becoming angry.