Heat oil in the instant pot on "saute" until it is hot and shimmering but not smoking. Alternatively, use a medium skillet over medium heat, about 2 minutes. Add onion and cook, stirring occasionally, until softened, about 4 minutes.
Add garlic, spices, and 1/2 teaspoon salt; cook, stirring constantly, until fragrant, about 1 minute. Add ground turkey and cook, breaking meat up with a spoon and scraping pan bottom to prevent scorching, until turkey is no longer pink, about 5 minutes.
Add the tomato sauce, chicken broth, brown sugar, and vinegar. Allow liquid to simmer, stirring frequently and breaking meat up so that no chunks remain, until liquid has reduced and thickened (mixture should not be completely dry), about 10 minutes. If using a skillet, bring liquid to simmer then reduce heat to medium-low and simmer, uncovered, stirring frequently.
Adjust seasonings with salt and pepper. Serve immediately, passing toppings separately. For taco salads, top cut lettuce with taco meat and toppings.