I can only imagine that this isn't necessarily working as intended...
If you attack something, your chocobo attacks it until the enemy dies or you give your choco another command.
For ACR/SMN pets, the pet will continue to attack each new enemy that you've attacked since then, even after the current enemy dies. It will even attack enemies who have attacked you, regardless of whether or not you've attacked it.
In the choco's case, after the enemy it was attacking dies, it will then sit there and do nothing until you actually attack an enemy while it was unoccupied.
This is especially annoying when you go to heal yourself after you've just killed one enemy but another is still attacking you: your chocobo will stand there watching as the enemy attacks you.
Is this working as intended or should the chocobo have the same AI that combat pets do?