Leveling up doesn't make you produce more Starbits. You have to buy fans for that. Leveling up only serves to open up islands and make more missions available. At level 15, ego kicks in, so start buying instruments. Read the game's help, which is quite clear, or the tutorials, which are plentiful.
@risingstargame/the-ultimate-rising-star-tutorials-list-en-es
RE: Starting The Rising Star Game - My Experience.