Heat 1/2 tablespoon olive oil in a large skillet over medium-high heat. Add the quinoa and cook, stirring, until lightly toasted, about 4 minutes. Add 4 cups water and 1/4 teaspoon salt and bring to a boil. Reduce the heat to medium and simmer until the water is absorbed and the quinoa is tender, about 15 minutes.
Toss the turkey with half of the herbs, 1/4 teaspoon salt, and pepper to taste; set aside. Soak the onion slices in cold water, 10 minutes.
Toss the tomatoes, chile, cucumbers, vinegar, 1 1/2 tablespoons olive oil, the remaining herbs, 1/4 teaspoon salt, and pepper to taste in a large bowl. Drain the onion, add to the tomato mixture and toss.
Heat the remaining 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Working in batches, add the turkey and cook until golden, about 3 minutes per side. Drain on paper towels, then cut into 2-inch pieces. Fluff the quinoa with a fork and divide among bowls. Top with the tomato mixture and turkey.