Personal trainers cannot perform massage or soft tissue work-this goes outside their ‘scope of practice’.
A trainer with a license for massage or hands on therapy can only perform procedures they have a license for.
NO MASSAGE! Unless the trainer has some other certification or license (i.e. Massage Therapy or perhaps Athletic Training as Joshua said). As LaRue said, it can vary state to state but most Personal Training certifications I’ve looked at don’t include massage in their scope of practice.