Is it common during a FUE procedure for technicians to do the some/all of the implanting?

The answer changes depending on the clinic you got the treatment. Some technicians are trained to play a part during the whole procedure. The information of your operation should be given to you before hands.

The implantation is performed by the technicians  under the supervision of the surgeon.

The technicians  implant the grafts on the channels. 
The incision must be performed by the surgeon to get the correct direction, angle and the distribution.

Doctor should be making all the incision where the hairs will go in the correct direction, angle, and distribution.Most cases, highly trained technicians insert the follicles into the pre-made sites.

In our practice the physician performs all of the extractions and graft placement, but this is not the norm. Legally in the US, physicians should be performing all of the FUE extractions, and at a minimum perform the incisions for graft placement. Many clinics use technicians to place the grafts into pre-made incisions, so what you experienced sounds both normal and legal.

The answer is no, it is uncommon for physicians to place grafts, especially all of them.  Most facilities rely on technicians to hand place grafts in premed surgical slits completed by the physician.
In my office, I core and place all of the grafts on every patient.  I use implanter pens that are loaded by one or two assistants and placed by me, using a stick and place technique with no pre-made surgical slits.  I feel that the healing and results are superior. My patients have a tremendous comfort level knowing that I will be placing each graft and that I am fully involved throughout the entire case.  In doing so,I am able to ensure that each graft placement is done in the correct manner and with the least amount of trauma. 
I encourage all prospective patients to interview their physicians to determine their involvement in the case to gain the greatest comfort level prior to making a decision on who performs it.

In my clinic I do all - extraction and implantation as well. I use implanters and technicians only load the tools. I know in other clinics technicians insert follicles and it is common.

This is common practice in the UK too. However, legally your surgeon should be the only person making any cuts/ incisions for technicians to implant hairs into. 

Your assumptions are correct. The doctor performs the harvesting and the incisions while the technicians perform the placement of the grafts.  This practice is both very common and legal.

It is legal and commonplace for technicians to place grafts after the physician surgeon has made the openings for them.  

Yes, it is very common for the technicians to perform all of the implantation. The surgeon must make the sites, control the distribution and the direction of the hair grafts sites as well.