Add tomato sauce to onions, and rinse can out with about half a can's worth of water; add water to pot. Boil sauce; keep an eye on it, because it won't boil like water (it's thicker and will splatter).
Once sauce starts boiling, add rice, onions, and salsa (you can add more later if you're afraid of adding too much). Cover and simmer for five minutes.
After five minutes, turn off heat, stir, and recover for an additional five minutes. Give it a stir, add in cheese; recover until rice is fully cooked or until you're ready to serve.