Anneke is 100% correct. Usually, there will be either a well in the cooktops that is kept just below boiling, or the responsible line cook will have a large pot of boiling water (refreshed as it boils down). As orders come in, a portion of par-cooked pasta is put in a receptable (that looks like a bain with lots of holes, with a handle) and dunked in the re-cooking bath. When it's done, it's pulled out, allowed to drain briefly, and then dumped into the saute pan with the sauce and other ingredients. Plated, finished with whatever, and ready to go.
I've never liked that dump in hot water to reheat method. Something about being impatient and not letting the pasta drain properly. I've always preferred heating it in the sauce. In the "old" days, they used to keep the pasta in cold water and whenever they needed some they just fished it out! I'm glad we know better now