It’s usually a little more complicated than that, as the loan itself and the payment don’t show up on your report the next day. Your score would have gone down because of an inquiry and a new account regardless of whether you paid it. Once you paid it off, it would have gone up a little (because of LTV going from 100 to 0), but the account history remains on the report for 10 years. I don’t see how it could’ve gone down.
Removing Negative Items from Credit Reports