Some physicians elect to be the "technician" on all technologies. Others appoint nurses or physician assistants to treat. Often, if a treatment has a high safety profile, delegating the treatment to other staff is perfectly fine.
Since Ultherapy is noninvasive, staff with experience and education are frequently just as capable - and since their time is less in demand, they can usually spend a bit more time with patients than a doctor who typically has a more pressing schedule.
As to having non-medical personnel perform the treatment, if you are uncomfortable with that option, then finding a practice that only uses medically trained technicians would not be hard. Or you could request a nurse to be your treatment provider.
In our office we elect to provide Ultherapy only by nurse, physician or physician assistant.