Both the fee of 350 and the sales tax on it are included in the payoff you get from that site. I sold my Accord to CarMax on 4/17 so I had my doubts too when my account showed the fee and the tax on it itemized in my payment history when they received payment from CarMax. However, I owe nothing now.
You could work backwards from the dealer payoff to get your base payment and verify your personal payoff in the HFS account too.
(Dealer payoff - residual value - disposition fee of 350 - sales tax on disposition fee)/number of payments left = base payment.
(Residual value + number of payments left * base payment from above)*(1+sales tax in %/100) = Your current payoff