In my experience, and I'm talking about bending welded or seamless cold formed tube, the bending is done around a tight fitting curved forming die with an equally tightly fitting follower pushing on the outside of the curvature, as distinct from a mandrel which goes inside the tube and is flexible.
The forming die is sized differently for various OD of tube (for example,I think 1.25" OD bright tube bends to a 4" c/line radius, though wall thk can be a factor) and the radius shown on the drawing is the nominal centreline of the tube. So, the radius is predetermined for each diameter of tube by the mfr. of the tube forming machine, though custom dies are possible.
I have no experience of CNC production tube formers, but I am pretty confident that here again the rad will be fixed by the former.
"The ideal client is one possessed of great good sense and perfect judgement;
that is to say, one who agrees entirely with the designer at all times and in every respect."
Fenwick Williams, Naval Architect.