Heat the olive oil in a skillet over medium heat; cook the onion and bell pepper in the hot oil until they begin to soften, about 5 minutes. Add the garlic and ground turkey to the skillet; cook and stir until the turkey is completely crumbled and browned, another 5 to 7 minutes.
Stir the pureed tomatoes, barbeque sauce, ketchup, vinegar, Worcestershire sauce, mustard, and chile-garlic sauce into the turkey mixture. Simmer until completely heated, 7 to 10 minutes more.
