In small bowl, combine teriyaki mix, paprika and pepper.
Coat the pork the with rub mixture, patting until all rub is used. Set aside.
In a bowl whisk together the chicken broth, brown sugar, soy sauce, chili sauce and pineapple juice. Set aside.
Put the chopped onions and carrots in a 5-quart slow cooker. Place the pork on top of the carrots and onions and pour half of the pineapple juice mixture over pork. Reserve remainder for Hawaiian sauce. Cover and cook on low for 7 to 8 hours. The meat should fall apart easily. Remove the roast from the slow cooker to a cutting board. Using 2 forks carefully pull the meat into shreds.
In a medium pot heat the oil over medium heat. Add garlic and ginger and saute until soft, about 2 minutes. Add the remaining pineapple juice mixture, bring to a boil, then reduce heat and simmer for 10 minutes. Remove from heat and set aside.
Serve the pork on rolls drizzled with the Hawaiian sauce or on the side for dipping.