It is controlling and coercive behavior. The implication is "We are in a relationship, you must cede your privacy to me". Matter of fact, of the abusive relationships I've experienced in my professional capacity (which is criminal law, so it's always bad), this is exactly the sort of risk factor that victims experience having brushed off early in their relationships.

I'm not saying this bloke is a monster, or that he is/will become an abuser, but frankly, if you can't trust your partner, and your issues are so deeply routed and become expressed through risk factor behaviors, then you shouldn't be dating them, or arguably at all until you have processed your trauma.