Heat a large nonstick skillet over medium heat. Add oil. Once hot, add onion and cook 3 minutes. Add turkey and cook 4 minutes, or until browned, stirring to crumble. Stir in tomato sauce and remaining ingredients. Bring to a simmer. Cook 5 minutes or until slightly thickened, stirring occasionally.
Divide turkey mixture evenly among bottom halves of buns; top with top halves of buns.