Animal training seems to be done on some kind of schedule much of the time, i.e. trainers won't go through their list and train the 'least tame' creature, but rather wait for some timer or whatever to tick and generate a new 'train animal' job.
As you said, trainers will quickly go and tame a wild creature, but reinforcement training happens slowly and in long intervals (long enough that a 'trained' animal can go semi-wild and completely wild before the next session is due).
Are your animals actually outside of cages? I have noticed that trainers will _never_ reinforce training of a currently-caged animal (but will train chained animals, i think); they'll re-tame them once they're wild, that's it.
If you lack confidence in your trainers getting to the semi-wild roc before it goes feral, you can simply order it stuffed into a cage. Then wait for it to go wild and the trainers should go and retame it.
Regarding domestication of animals - if an animal _species_ is listed as 'domesticated', a single training session will domesticate an exemplar taken from the wild. They only present a minority of animals you'll encounter, but e.g. the water buffalos found in subtropic/tropic wetlands will become fully 'tame' when tamed by an animal trainer.
I'm not totally certain, but i think it's the 'child' status that makes fort-born animals tameable - i.e. a pup/cub/kitten/child of an animal can be made fully tame with a successful training job, regardless of whether it started at *trained* (born from a half-domesticated mother) or wild. An animal child which did not receive training before becoming adult cannot be made fully tame.