I understand your situation, but I think the solution needs to come from your end rather than trying to change standard protocols. Imaging and other diagnostic testing is typically done by technicians who are experts in the process and equipment for their areas of expertise. It is more of a mechanical process than a medical one. To have doctors available on site for no particular reason would just be cost prohibitive and they could not stay in business. Think of it as having a cardiologist living you your home just in case you had a heart attack. It is pretty much the same situation. I'm sure all imaging centers have a protocol for calling 911 if a customer has an allergic reaction to contrast (or has a heart attack) while at their facility. As them about that protocol to callm your fears.
You will have many situations like this throughout your cancer treatment journey, so you need to somehow find a way to be able to deal with it. Hopefully your psychologist can help you with that, but keep in mind, he/she is not a medical doctor either.