Fill a large pot with lightly salted water and bring to a rolling boil. Add tortellini and cook, stirring occasionally, until tortellini float to the top and the filling is hot, 3 to 5 minutes. Drain.

While the tortellini is cooking, melt butter in a large skillet over medium heat. Add onion; cook and stir until soft and translucent, about 5 minutes. Mix in spinach, cream cheese, mushrooms, Parmesan, and milk; stir to combine and cook until cream cheese is melted and mushrooms are soft, about 5 minutes.

Gently mix tortellini and cherry tomatoes into the skillet; cook until heated through, 5 to 10 minutes.