In New Jersey the sealt belt law is now a primary offense instead of a secondary offense as it used to be in years past. Because of this being an offense that will be listed on your driving record if could affect your AIG insurance premiums.
Insurance companies handle traffic violations and the points associated with them differently. In some cases a small infraction might removed your discounts while in others there could be a rate change or no change at all. Since this is your third violation of the NJ Safety Belt law it could indeed cause your rates to rise.
To be certain you can contact AIG and ask about their rating rules regarding this. Or you can contact the New Jersey Department of Banking and Insurance to find out their rating system since all insurance companies must file their rates with their state's regulatory body.