It's been a few years since I went through the polishing training with Rolex, but at that time there weren't any special machines involved. Just a variable speed polishing motor (a Ray Foster was their preferred brand), various buffs (Artifex, hard felt, unstitched cotton, and Bufflex for satin finishing), and Rolex does use Menzerna compounds that are specifically formulated for them, but those are commercially available as well.
There are some specific fixtures for very specific tasks, for example refinishing of Yacht Master bezels, but not for cases generally. The case work was all done by hand.
