Young players will develop in both, the Minors and Majors. But you have to be careful! If you put a young player to early into the majors, you might hinder him to develop to his full potential because he is not ready for the Majors.
I always take my time with young prospects. If I think one is ready (he has good enough ratings) I will call him up when someone from the Majors gets hurt. Then I play him a few days as a utility guy and watch his stats (and morale!). Most of the time I will send him back down after the injured player is back. Then, during September, when the Active Roster expands to 40 men, I get all my young player up to give them some playing time. Obviously only if I'm not in a Playoff race.
Hope that helps. If you have any other questions, just ask, I or someone else is happy to answer them.