Your 100% right.
He needs to calm down and let her mingle in with the other housemates, if not... well, I can see their relationship is going to go down-hill and she is going to be left with no girlfriend for the outside world.
Example... when they were doing the task he was dancing near her, but on the other side of the divide, she kinda moved towards other housemates but he just followed
.
Another example... when you said about Nicole wanting to go bed and he says 'I don't want you to go to bed'.
Rexy needs to take the chill pill.