Glad to know I'm not alone. And that it might not actually have to do with pet tamer battles. As I don't leave Pandaria for much else I don't have a wide net of experiences to go on.
Please, please, please, please, please, for my sanity, everyone report this as a bug when it happens and mention where you are leaving and going to so that they don't think I'm the only one with this happening. 15 minutes to wait for that cooldown isn't much in the scheme of things, but it's a lot of time when you want to get other things done.