You did not mention your state but 45 states and the District of Columbia are members of the Drivers License Compact which requires members to inform the state where a driver is licensed of any moving violation received out of state. New Jersey takes part in the DLC and if your home state does as well then NJ courts will notify your home state's Department of Motor Vehicles of this out of state violation.

Even the states that are not part of the DLC (Georgia, Massachusetts, Michigan, Tennessee and Wisconsin) may still be informed of the New Jersey ticket since many of these states have their own agreements with other states regarding the sharing of ticketing information.

To find out for certain if your state receives in violation convictions from other states and if what they do with that information (add to your driving record, assign points, etc) contact your state's Department of Motor Vehicles.