There is probably a dozen ways to do it. You can use a custom made shouldered rivet, you can use a drilled rivet that the bottom of the drilled portion is a specific depth so when it is rolled over the punch will bottom out, you can use the orbital riveter which is more than likely how that is done. An orbital riveter is depth adjustable. You can go the shim route, rivet the part tight, then remove the shim, you can have a rivet fixture that has a predetermined depth to it, it can be done in a die shoe with a nest that will rivet all the rivets at once to a predetermined depth, AND probably a few more ways.
I've made literally thousands of punches for an orbital riveter, and for hand riveting. It all depends on the part, the rivet, how many rivets, and how many parts are going to be made to determine as to how you want to do it.
A drilled or semi-tubular will hold the body size while the rest is rolled over. A solid rivet will swell out on the complete body. An orbital riveter is normally used on solid rivets, but can be used on tubular rivets.
Believe it or not, there is an art to riveting things. It's not just grabbing a pop rivet and a rivet gun.
