Partially freeze tenderloins; trim fat from tenderloins. Cut tenderloins diagonally across grain into 1/4-inch-thick slices.
Cook half of pork in 1 tablespoon hot olive oil in a large skillet over medium-high heat 3 minutes on each side or until pork is lightly browned. Remove pork from skillet, and keep warm. Repeat procedure with remaining pork slices and remaining 1 tablespoon olive oil.
Drain oranges, reserving 1/2 cup liquid. Add reserved liquid, orange rind, and next 3 ingredients to skillet. Return pork to skillet. Bring to a boil; cover, reduce heat, and simmer 4 to 5 minutes or until pork is tender.
Transfer pork to a serving platter, using a slotted spoon. Set aside, and keep warm. Add chutney and green onions to pan drippings. Combine cornstarch and water, stirring until smooth. Add cornstarch mixture to chutney mixture. Bring to a boil; reduce heat, and simmer, uncovered, until chutney mixture is thickened and bubbly. Stir in oranges and pecans. Cook over medium-low heat until thoroughly heated. Spoon sauce evenly over pork.