I started a fictitious league with a fantasy draft, and all the active rosters in the league only have 12 players and there doesn't seem to be a way to add more, did I make a mistake somewhere or is that how it works with that set up?

If you are running a team you should see a "handshake icon" in the upper menu bar - that is the button to sign free agents which you should be able to do once the season starts.