We made sure to feed all of these pets immediately before testing, insuring they were wonderfully happy. We tried bonded and unbonded pets.
We then tried pets that DID NOT need taming to control: forest ostards, swampies, horses, and fire and giant beetles. None of these went wild.
This seems to ONLY happen to pets you are RIDING, that require taming to control.
For example, I was riding my fire steed and also had my frenzied ostard with me. When I gave the follow command (all follow + target, NOT all follow me) the fire steed went wild, but the frenzied ostard was fine. Interestingly, this happened when I targeted a monster, myself, another pet, and another player, but NOT when I targeted an item in my backpack.
We assume that this will also happen with dread warhorses and bane dragons, but for obvious reasons would prefer not to test that