Help Please....out of state NJ lease tax

I leased a 2018 Volvo S90 from Massachusetts to be registered in NJ.

58500 msrp
10% off before incentives
9k incentives including volvo cash and Costco
Final sales price was around 43k
I got the payments to 355 a month

I signed all the contracts a week ago and now the dealer is telling me the taxes are wrong. What am I supposed to be paying for tax on this lease?

Is it on the total for the purchase price?
Is it on only the sum of the lease payments? Does this include acquisition? What about incentives?

Also… what is the luxury tax? My sales price including all incentives is below 45k… but without the incentives it’s over 45k… what do I pay in NJ luxury tax?