I tamed one of the Terracotta Quilen while on the quest to kill them and the mogu. I tamed him while he was active and moving. Once the tame was finish however he turned to stone and will not do anything.
This is a known bug with them. To get one that works you have to tame it while it's stone (you can do that ).
The reason seems to be that those beasts are on a cycle of flesh and stone, controlled by a couple of buffs. The flesh buff has a timer on it, and when it ends it triggers the stone buff.
When you tame something, it strips it of buffs. In this case it causes the flesh timer to end, thus triggering the stone buff. Since the stone buff is applied just after the buff check has happened it's never removed.
At least that's how it seems to work to me.