M.W.
Sounds like you're doing good already. I'd wait and see if he goes back to sleep in a few min like you did the first time he woke up. Many babies are light sleepers and its easy to wake up. If you do need to go in there, try not to feed him and keep the "reward" of you coming to him to a minimum, no lights, talking. Make a clear distinction that this is night time not day time. Maybe switch from soft music to white noise like a fan (this helps my girls a lot!)
No I don't think he's hungry, and feeding him is just rewarding him for waking up.
Best wishes, stay consistent and he'll get it! And don't be afraid of letting him cry a little, parents who can't let their kids cry end up manipulated a lot!