If you smack them down after their faction goes to war, you can imprison people who flocked to their banner. The peace settlement will only automatically imprison people who were members of the faction when it was put into action. Those people may be members or leaders of other factions if they disliked you enough to join a civil war against you which is why it may be confusing.
You should also be able to revoke titles from them if you have Limited Crown Authority or higher.