Sorry if I'm misunderstanding (I don't do a lot of hunts), but to give you an answer, as far as I know you don't have to pop the hunt monsters, they just spawn by themselves.

If you're popping something with a map then it sounds like you're doing a treasure hunt in which case you won't get allied seals and will just get the contents of the chest afterwards (which is applicable for anyone in your party so it should be agreed in advance who's getting what!)

If things have changed or I'm wrong, I'm sure someone will correct me though!