Cook spaghetti in salted boiling water until al dente per package directions. Drain, rinse with warm water, and set aside.
In a large bowl, combine softened cream cheese, cream of chicken soup, cream of mushroom soup, milk, onion powder, garlic powder, and diced tomatoes with green chilies. Stir until smooth.
Add shredded chicken, half the cheddar cheese, and half the processed cheese to sauce. Mix until chicken is evenly coated.
Add cooked spaghetti to sauce mixture. Fold together gently until every strand is coated.
Preheat oven to 350°F (175°C). Grease a 9×13-inch baking dish. Pour spaghetti mixture into dish, spreading evenly.
Sprinkle remaining cheddar and processed cheese over the top for full coverage.
Bake uncovered 25-30 minutes until cheese is melted and bubbly. Optional: broil last 2-3 minutes for golden crust.
Rest 5 minutes before serving to help cheese set.