Most of the time it is better if the client ask the therapists although some are afraid to and so therapists sometimes offer if they have picked up that the client would benefit but doesn't feel up to asking.

I don't think anything should be initiated by him without explicit or implicit permission from you. And if improper touching is a topic of concern in current sessions it is best that the therapist show lots of respect for boundaries, space, and all of that.

It doesn't sound like this person is trying to do anything wrong, but it does sound like he could be a little bit more careful.