This is directly from the manual:
Expansion drafts generally run for 35 rounds. Expansion teams must populate the remainder of their rosters by trades or through free agency.
http://manuals.ootpdevelopments.com/...ague_expansion
When you did finish draft, all it does is finishes the remaining rounds, it does not just draft until you have filled up your roster.
To fill up your minor league teams without having to sign players, you can go into Commissioner Mode and then go to the Players page of each minor league level and there is a button in the top right that says "Fill team with fictional players". It will generate players to fill out the roster, but you will still want to sign some on your own to cover injuries. Another option that will help keep them full is to allow minor league managers to sign/release players in the Manager Settings screen.