MLB can move them during this phase. from lolgatom's blog

Each move in Conquest mode is broken down into four phases: 

This is where you send your fan base out to take over empty tiles on the map, or attack a tile belonging to another team. If the space is free, you will automatically take it over. If it’s occupied by another team, you can choose to either “Simulate Game” or “Play Game”. 

Under the “Simulate Game” option, you’ll see a gauge that will tell you your teams probability of winning the matchup, which is determined by the Fan Distribution shown at the top of the screen. This shows how many fans you are attacking with, and how many of your opponent’s fans are on the tile you are attacking. The more fans you have, the higher likelihood of you winning a simulated matchup.  

If you decide to “Play Game”, or if you are attacking a team’s stronghold (their home base) where “Play Game” is required, you’ll have to select a difficulty level to play the game on. The available options are determined by the Fan Distribution. The more fans you have attacking, the lower the difficulty you’ll be able to play on. 

Win the matchup either by simulating or playing, and you’ll take over that tile and it’s fans. Take over all the tiles, and you’ll win Conquest mode.

After each Attack Phase, you’ll be given the opportunity to steal fans away from any remaining team’s stronghold. You just decide which team you want to play, and then choose the difficulty level. The higher the difficulty level you decide to play on, the more fans you’ll steal if you win the game. Cheap MLB18 Stubs 

After you’ve completed the Attack and Steal Phases, you’ll get to place fans you’ve won on any of the tiles that you have control of on the map.

If you have an excess of fans on a tile, you can move them during this phase. Once this is completed, you’ll go onto your next move, and go back to the Attack Phase.