For the first time one of the captains you have dominated is captured, you will get a notification screen. You can also spot a captured captain on the army page by a special sign above their heads (they will be standing on their knees).
If you want to enforce a rescue mission, dominate a bunch of captains and send them to kill others. Keep advancing time and eventually, one of them will be captured. You may have a higher chance of getting a rescue mission if you send a low-level captain to kill a high-level one.
When you start the rescue mission, you can try to go stealth and cut the rope from behind the captured captain. In my experience, this is not that easy and I failed on my first try. On the second try, I went berserk and killed all the enemies as fast as possible which luckily worked. Note that, you need to kill the enemy captain in both approaches in order to get the achievement.