OK, so it is only in this set phrase, then (di rumah) that the word rumah means home, otherwise it means house?
Is there a difference between "you are at home" and "you are at the house"?
No, rumah is both house and home. Typically you'd qualify whose house by saying something like "Aku di rumahku" (ku being a suffix added to nouns to show possession and is short for aku). Or similarly, "Aku di rumahmu" (in this case -mu being short for kamu)