The good news is that the certified letter, if you sent it to the address in your contract by the deadline for rescission in your contract, is going to take care of cancelling your recent purchase. The salesperson is just trying to scare you into changing your mind. You never had any equity to give up. When salespeople talk equity, they're really talking the worth they give your timeshare if you're trading it in to purchase a different type/location of points. It doesn't have any value/equity in the real world.
So if the salesperson is trying to talk you into signing or agreeing to something, just disregard them. If they insist, I'd simply state something like, "I assume the rescissions department at corporate will contact me to take care of this step when they receive my letter." (They will not, though, because it's not necessary and just a sales scare tactic.)