According to the New Jersey MVC (PDF), if you purchased a vehicle in another state and paid sales tax on the vehicle, you provide MVC with the receipt. If you paid 7% or more sales tax in the other state, you pay no sales tax to New Jersey. If you paid less than 7%, you pay the difference to New Jersey. In practical terms, if the purchaser buys in the states neighboring New Jersey, there is no additional cost — New York State sales tax is 4%, Pennsylvania sales tax is 6%.
For example: Alice, who lives in Atlantic City, buys a Tesla in middle-of-nowhere Pennsylvania (6% rate) for $60,000. Alice pays Pennsylvania sales tax on that vehicle in the amount of $3600. If she had purchased the vehicle in New Jersey, she would have to pay $4200 in sales tax. So when registers her vehicle with the MVC, she'll owe the difference ($600), plus title fee ($60) and registration fee ($59 assuming it weighs under 3,500 pounds, see here), and possibly, if Christie is really an a-hole, a 0.4% Luxury Surcharge ($240). Keep in mind, if she purchased the vehicle in New Jersey, she'd pay the same sales tax, but all of it would go to New Jersey. If she purchased the vehicle in New York (4% sales tax), she would pay $2400 in tax to New York and $1800 in tax to New Jersey.
But, I could be missing something. If so, please let me know.