What I am about to say is not legal advice. it is purely for informational purposes and is based on hypothetical facts. You should consult an attorney familiar with your particular facts and circumstances who can provide specific advice regarding your particular situation.
Having said that, what happens when someone is convicted in another state, say NY, is that the court in NY sends a record of the judgment of conviction to the MVC in NJ. If the MVC feels that there is an NJ violation that is similar enough to the violation in NY, they can give the person the number of points that the similar NJ violation would carry.
So, for example, say the person was convicted of Careless Driving in NY. In NJ, careless driving carries 2 points, so the MVC could (but doesn't have to) give the person 2 points on their NJ license.