lease buyout question..?

I traded in a leased vehicle today before the lease was up. The lease was with Toyota Financial and I still had 30 months left in the lease. The dealership I traded it in at asked me for the payoff amount to own the vehicle outright, so I went on toyota financial's website and it showed the buyout was 31,597.00 HOWEVER, this amount did NOT include sales tax. The dealer was aware of this and they did not charge me the sales tax on the buyout amount. All of the paperwork I signed shows that the amount for the payoff is 31,597 and that is how much they are sending to toyota financial to request the title. When they get the title am I going to get a bill for the tax on the lease? I am SO confused on this. The business manager assured me that I won't hear another word on the matter, but I'm still concerned. There is nothing in writing stating that I agreed to pay them the sales tax...I did pay the sales tax on my new vehicle but thats it...will this become a problem? I hope I made this clear enough for everyone to understand...let me know if you need any clarification as the whole process is very new to me. Thanks!