Preheat grill to 350-400 degrees. Remove silver skin and excess fat from tenderloins. Brush tenderloins with oil and rub with jamacian jerk seasoning, salt and pepper.
Grill tenderloins, covered with grill lid, 8 to 10 minutes on each side or until a meat thermometer inserted into the thickest portion registers 155 degrees. Remove from grill and let stand 10 minutes.
While tenderloin is on the grill, combine ROWENA’S jam, dijion mustard, ginger, and rum and heat on medium heat until mixture thickens slightly. Season to taste with a pinch of salt and pepper.
Slice pork and place on serving dish. Pour sauce over pork.