Fill a large pot with lightly salted water and bring to a rolling boil; stir in tortellini and return to a boil. Cook uncovered, stirring occasionally, until the tortellini float to the top and the filling is hot, about 3 minutes. Drain and set aside.

Meanwhile, toss diced sausage in a nonstick skillet over medium heat; cook until edges are browned, about 3 minutes. Remove from heat and set aside.

Pour Alfredo sauce into a saucepan. Add milk to any leftover sauce in the jar; shake it up and pour into saucepan. Stir in Parmesan cheese.

Warm sauce, stirring often to avoid scorching, over medium-low heat, about 5 minutes. Add sausage and tortellini, and cook just until heated through, about 3 minutes more.