For rub, in bowl, stir together brown sugar, paprika, garlic powder, pepper, salt, and cumin. Sprinkle over both sides of ribs; rub in with fingers. Cover; chill for 2 to 24 hours.
For charcoal grill, arrange medium-hot coals around a drip pan. Test for medium heat above pan. Place ribs, bone sides down, on lightly oiled grill rack over drip pan. Cover; grill 1-1/2 to 1-3/4 hours or until ribs are tender. (For gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking. Place ribs in a roasting pan. Grill as above.)
Meanwhile, for sauce, heat oil in saucepan over medium heat. Cook and stir onion and garlic in hot oil 5 minutes or until tender. Stir in tomato sauce, rum, molasses, Worcestershire sauce, vinegar, dry mustard, and chili powder. Bring to boiling; reduce heat. Simmer, uncovered, 20 minutes or until sauce is reduced to 1-1/2 cups, stirring occasionally.
To serve, cut ribs into six portions or individual ribs. Spoon sauce over ribs. Makes 6 servings.