Place pork in a gallon zipper bag. Add 1-cup teriyaki sauce. Seal the bag, and turn to coat the meat in the teriyaki sauce. Refrigerate and let marinate at least 30 minutes.
Heat grill pan or outdoor grill over medium high heat.
In a medium sauce pan, combine rice, pineapple juice, water, butter, salt, pineapple tidbits and salt. Heat over medium heat until boiling. Reduce heat to medium-low, cover, and simmer 20 to 25 minutes until liquid has been absorbed.
Remove pork from marinade. Thread pork slices onto skewers.
Grill for 2 to 3 minutes per side, until pork is cooked through. Remove from grill and loosely tent to keep warm.
Fluff cooked rice with fork and stir in cilantro, scallions and lime juice. Serve pork and rice hot. Serves 4 to 6.