The factory update was when in 2002 they made the shift gates wider in an effort to prevent blown engines from misshifting. Your shifter should fit because your car is a 2001. BTW, I have the TRD quickshifter and I LOVE it. One of the best mods I've done.
Even if they dont match with the factory updates, its just shifter linkage that you would replace, and its not a "necessary" modification. changing the linkage only makes it "feel" a little different. I used to work at a Toyota Dealership, and looked into this after having my tranny replaced (the guy that owned my car before me didnt know how to drive a 6-speed). I have the TRD
Short-shifter, and there is no way I will ever own a manual transmission car without this mod. I love it!!! Excellent feel!!!