Make the picadillo: Heat oil in a large skillet over medium-high heat. Add onion, and cook until just starting to turn translucent, 3 to 5 minutes. Add turkey, and cook, breaking up pieces with the back of a wooden spoon, until browned, about 4 minutes. Stir in garlic, tomatoes, paprika, chili powder, oregano, salt, pepper, and cumin. Add water, and bring to a boil. Reduce heat to medium, and simmer until thick and very little liquid remains, about 18 minutes. Stir in vinegar.