Bring a saucepan of lightly salted water to a boil, stir in the tortellini, bring back to a boil, reduce heat, and simmer the tortellini until they're cooked but not completely tender, about 5 minutes.
Drain the tortellini in a colander set in the sink.
Preheat oven to 325 degrees F (165 degrees C). Grease a 1 1/2-quart oval baking dish.
Heat the butter in a skillet over medium heat. Cook and stir the garlic until fragrant, about 2 minutes.
Whisk in the Alfredo sauce and milk; season to taste with salt and pepper. Bring the mixture to a simmer over medium-low heat. Stir in the the tortellini and turkey, mixing just enough to coat the pasta and turkey with the sauce. Spoon the mixture into the prepared baking dish, and sprinkle the top with mozzarella and Parmesan cheeses.
Bake in the preheated oven until the casserole is hot and bubbling and the cheese topping has melted and begun to brown, 15 to 20 minutes.
