I suspect crewmembers are "assigned" to room only when they reach their destination within the room.
I decided to wait till teleport would go of cooldown since enemy ship aiming system was suppressed. I assigned mantis on enemy ship to attack shield systems. After some attacks of said mantis on shield systems enemy ship exploded (even tho it had previously 1 hp).
Result: lost 1 trained mantis

Hope this is not a feature (e.g. teleport that transfers only idle crewmembers)