How does taming wild animals work?

I have:

• dwarves with the "Animal Training" labor activated
• a trapped wild animal in a built cage, inside an animal training zone
• one of the available dwarves selected as trainer on the [z] - Animal page
• both plant and meat food

All my trainers will do is train the animal to semi-wild, and that's it. After a while, it'll revert to wild, and the process repeats itself. They already did that when the cages in question were stored in my stockpile, neither built nor in a training zone - so I thought putting them there might make my dwarves continue the training and enhance the level of domestication.

Am I misunderstanding how animal training is supposed to work? What should I be doing differently?

EDIT: Apparently, a caged animal will only be trained to semi-wild, and needs to be put in a pasture or on a restraint afterwards to increase the level of domestication!