Are nurse practitioners in CA allowed to do off-label uses of fillers with no physician on site?

First I am so sorry you received what sounds like a very unpleasant service.
Nurse practitioners should be working under the supervision of a physician who may supervise up to 4 nurse practitioners. The supervision does not need to be direct nor does the supervising physician have to sign off on the medical record of the nurse practitioner. The supervising physician and nurse practitioner are suppose to work under written treatment protocols. So a nurse practitioner can legally provide the service you received. The issue of what is on and off label is complex.  These fillers are FDA approach for subcutaneous placement.  The undereye area constitutes a complicated subcutaneous treatment area.  Many physicians also do a poor job of treating this area.
I strongly recommend that you only go to injectors whose reputation and capablilities you thoroughly understand.  Perhaps you chose the clinic you went to because the price was right or their marketing was attractive.  Do your homework and find a practice that is right for you.  For example in my office, I do not use nurses or physician extenders for services.  I do all the work myself from surgery to filler and botox services.

nurse practitioners can do procedures such as fillers and the overseeing doctor does not have to be present BUT the other part of your question No one is approved to inject off label uses