In order to use automatic prisoner transport a Police Supervisor (US) / Senior sergeant (AU) is needed in the mission. After the mission ends vehicles of all players that have a olice Supervisor (US) / Senior sergeant (AU) at the scene will automatically transport prisoners to the nearest free cells.

You can select in the settings if they should only be transported to your own cells or also to alliance prison cells.
Vehicles of the mission owner are prioritised and vehicles that can carry more prisoners will be used before vehicles that can carry less prisoners.
Vehicles that transport prisoners will return to the place of the mission afterwards as long as there are prisoners that need to be transported.

Prisoners are not transported immediately after the mission ends, so that the mission can stay open for other alliance members for a while. This time is set to 10 minutes per default, but can be changed in the settings of the Police Supervisor for this particular vehicle only or globally in the settings of a dispatch center,

You can also disable automatic prisoner transport in the dispatch center settings or individually in the vehicle settings.