Most auto insurance policies include a broadening clause that raises the liability limits to the minimum of the particular state that a driver is operating a vehicle in and thus conform to the minimum limits of that state compare to their home state.

You would need to contact the at-fault driver's insurance company and see if the person's property damage liability coverage has this clause and will conform to the $10,000 minimum PDL limits instead of the lower New Jersey $5,000 limit. 

If you have questions about how the claim should be made and need other consumer advice about your situation, contact the New York insurance department since it appears the accident took place in NYS.