Originally posted by Some Kinda Kobold:

Taming seems to pause if no one is in render distance of it.

Otherwise it takes a REALLY short time and you only need to do it like, twice per animal.

"really short"? Everytime I've tried its taken 30-40 minutes realtime. Maybe I was doing something wrong.

Also, if its not being rendered odds are the game isn't going to be updating anything in that area so you should always stay in render distance at minimum. only exceptions I can think of would be groth of planted items, and progress of mechanicals like smelters, windmils, etc.