Okay this may be a stupid question, but do pets break crowd control?

Yesterday I did Stone Vigil for the first time and I had emerald carbuncle out. The healer said that he wanted to sleep the adds and we would attack enemies one at a time. I remembered people on the forums saying to just put the pet on Obey. So I tapped Obey, and we got through half the instance just fine before we wiped.

When we did wipe, I re-summoned my pet and hit Obey, only to realize that Obey is not a permanent state like Guard, and that you have to hit it while targeting something. So on next mobs I am freaking out thinking that my pet is gonna wake the enemies up. Somehow the enemies woke up. Even though the archer took credit for waking them, I was still unsure if my pet did it.

So I went through the battle log, and saw that my pet had been using Gust through the whole dungeon, so it wasn't the pet's fault. But now the question is why was the pet only using Gust and not its other abilities?