I only got the pilot bearing with my Exedy kit. It doesn't fit anywhere, and my car didn't have one installed when I first took it apart. I had to align the clutch without the tool by hand...which I somehow managed to do. I'm not sure about the rubber thing that you mentioned. If you use the rubber thing and leave it in there, make sure it's seated very firmly and won't fly out later on.
2000 GTS 6-speed. Performance Mods: Apexi Power FC, BC Racing DR coilovers, Injen CAI, Catback exhaust, EBC 'USR' rotors, Hawk 'Street/Race' pads, Stoptech brake/clutch lines, Castrol SRF brake fluid, Exedy stage 2 clutch, Mishimoto radiator, Moroso oil pan, 11# flywheel, Braille 11.5# car battery, Energy urethane suspension/motor bushings, BFGoodrich G-force tires.