Unfortunately, the taming of both mounts is strictly related to the story missions. Thus, you will receive a flying griffon and a dromarog moving on the ground automatically. Dromarog will be completely unlocked towards the end of the game!
As for the rest of the animals, in the future you will receive a grab-bag and you can catch them, and then sell them or put them in special reserves inside the help-room.
The action game also received a content update.