Those are things that some of us will let them do around us, but they're not always comfortable with that. They want to be alone and only want us around when it's convenient. If he stays there with you, your relationship could get worse. You have to give him props for at least telling you that this will make things better for the two of you. He'll miss you more and eventually he will want to live with you again.
Distance makes the heart grow fonder.
Enjoy your time alone. I know it's hard at first, but don't think about what you're missing, think about all of the time you'll have to yourself. If he's cheating, which it doesn't sound like he is, then you will know right away. Invite yourself over to his new place and tell him this new living arrangement will be fun because you two can start dating, which is something you two probably never got to do since you moved so fast. It will be hard, but try not to sweat it.