Kohler is notorious for having wacky different parts instead of standard ones, particularly flappers and fill valves, and not being receptive to parts from other companies. Most one-piece toilets, however, don't just accept the kind of fill valve you purchased, anyway.
Reach has done you a favor by getting you the exact part number you need. There are about 20 different flavors of Rialtos over the years, and the parts change from one to the other, even though it is called the same thing. That's why the model number (the one with the big K in it -- for Kohler) is important in finding the right part. You can't just get a "Rialto Flush Valve". You need the right one, so follow his lead carefully.
Looks like you want the 83650, but you should double-check. Type Kohler 83650 into Google, and pick your supplier, or go by a local plumbing supply place.