Submissive Behavior?

Hi,

I have taken Rocky(9 month old male) through obedience class and he fared pretty well. My biggest problem has been trying to get him to come inside after we play in the backyard. I will tell him to stay and walk after him calmly. He has started to go into a lay down position when we start to do this. Is he really staying for me or is he just being submissive? Not sure if it's a big problem, but want to make sure he is getting the right message.