There is no technical reason to mix lidocaine into Radiesse, but it makes the injection much more comfortable. I don't use 4cc of lidocaine though, so I wonder how many cc's of Radiesse you had.
In general, I use enough lidocaine to thin the Radiesse and provide pain control, but by the time the patient has iced for 10 minutes after the injection, there is minimal volume increase from the amount of local anesthesia I mixed in. Remember too that some patients swell just from having the product injected, so the volume of the local anesthetic may not be the only reason that you were visibly swollen.
Ultimately, you should be able to discuss your concerns with any physician you are considering allowing to do these injections. Make sure it is someone with good training and a lot of experience, they should be fine addressing these questions with you.