Pen Makers build their caps and rings in different ways. In the old days (think late 1800s/early 1900s) many makers swaged rings onto caps. Essentially squishing very thin rings into little grooves on the cap.
This video goes into pretty good detail about swaging.
This is gear from the old Omas factory, where they swaged cap rings onto caps, with the 3 handled collet tool you can see bolted to the table here-
The part would be inserted into the collet (the hole in the middle) and the handle would be turned, closing the collet, compressing the ring onto the part.
Many makers today will build caps with a layer of rings over a tenon.
Companies with injection molding machines (Montblanc/Omas/Pelikan/Pilot and others) will mold the rings into the caps…
Sailor glues rings over tenons, too. You can see the tenon on the cap at top right of this photo.
and Maiora. You can see the layered rings pretty easily here – the ebonite pattern and colors are different from main cap to each ring, and on the left side you can see the light beige ebonite inside the cap, and that the ring is mostly blue.
There’s a couple ways to do the layered rings, but this is my preferred way now days. I used to do it a little differently. The cap lip has a tenon, and the ring is sandwiched between that and the main part of the cap.