You will definitely fall under the jurisdiction of the Court in NJ for anything related to the DUI, i.e.; jail time, fines, order of license suspension. PA will automatically suspend your license under PA state law, and will add anything the Judge in NJ stipulates as punishment from NJ, i.e.; 2-3 years suspension, having a B.A. machine installed on your car, etc.
Should NJ consider probation, they may allow you to transfer your probation to PA, and then PA would monitor your probation for NJ, but NJ will retain jurisdiction of your case. If PA reports to NJ that you are a screw-up while on probation, you can be ordered back to NJ to finish up your term of probation, and/or revocation of your probation, to have to serve the time in jail in NJ.