The Fall leagues I think you are talking about are by invitation only. One is Fall instructionals. Each team invites 40 players to their Spring Training facility for about 3-4 weeks of work.
The second is the Arizona Fall League. Each team sends 6 players. The Winter leagues are usually at the suggestion/arrangements of the team although not completely. Some players do that on their own if they can find a team.
In terms of improvement, most players will not even pick up a ball from the end of the season until December. Use that time to rehab as well as to lift and condition. The organization will provide a workout schedule and periodically check on the player. The player however is on his own in terms of strength, conditioning and being baseball ready when Spring training begins. Part of being a professional. The improvement is during Spring training and every single day of your 144 game schedule.