The tough part of conveying emotions through music is that you don't have 100% control over your development. As you grow, music opens up to you. Your music grows with you.
I think that's why you can't put an age on "mature musicians". Everyone has a different life story, with different experiences, joys, pain, and losses. Some kids go through much more in their short life span thus far than some adults who are well into their 50's or 60's. Whenever I watch some convey passion and emotion through their music, I always end up wondering what life has shown them that has brought them to this point.
You might find that upon revisiting music that you played when you were little, that there are new sides to the music that you never noticed before. It's kind of like watching Disney movies when you're older--you get a lot more of the jokes that completely went over your head when you were a kid. You get it now.
It's the same with music. :)