Trim fat from tenderloin; cut tenderloin into 1/2-inch-thick slices.
Combine thyme, allspice, and ground red pepper. Sprinkle half of spice mixture over pork slices. Coata large nonstick skillet with cooking spray; place over medium heat until hot. Add pork; cook 3 minutes on each side or until browned. Remove from skillet, and keep warm.
Increase heat to medium-high; add 1 cup onion and next 3 ingredients, and saute until crisp-tender. Add remaining spice mixture, broth, and next 3 ingredients. Arrange pork over bean mixture. Bring to a boil; cover, reduce heat, and simmer 10 minutes or until pork is tender. Stir in lime juice; sprinkle with green onions.
Combine rice and turmeric; toss well. Serve pork mixture over rice.