Should be compatible with everything, but pay attention not to: See the tutorial video if you're having any issues
If one dies it is immediatelly unregistered and a slot frees up. They are not set essential and can die, so you need to take care of them. Up to 50 animals can be managed at a time and there's a simple option to permanently dismiss if you don't want it any more.
Reason for this is largely technical, since dialogue options require adding voice types to animal NPCs which is much too invasive/complicated to implement. Tamed animals become potential followers, you can set their homes, make them wait/follow just like any standard follower, major difference is that they're commanded via a menu instead the dialogue.