I've seen much older posts about this, and there is an item in the FAQ that says the fix is to update beyond 1.6.3. I'm running 1.6.4 on my iPad, and I am not seeing the star appear next to a level type on the "Choose Level Type" screen in Arcade mode after I've completed all the levels of that type.
The behavior is not uniform, however. The star appears for Ambient and Sentient, but not for Antimatter, Impasse, or Replusor. I have not gone beyond this point in the game. I have not completed the level types in the sequence in which they are listed, if that helps.