To the best of my knowledge, having tamed probably 100's of Valheim's wildlife, to progress the acclimatization process, one's character needs to be in close enough proximity for the taming emotes to be emitted. Having visual contact with the animal being tamed is not necessary, but being close enough to be able to is.

Similarly, tamed animals only breed when one's character is in the vicinity. To ensure tamed animals reproduce, have them in close enough proximity to one another for their happy feeling emotes to burst forth from their bodies. Tamed creatures will not breed & reproduce if a player throws down food then zones out before copulation occurs.