Not by aegis-botherers though (unless they're led beyond the aegis, engaged, then led back - even then, it's not certain).
You can encourage them to start their attack by hitting them once as soon as the station and police is out of scanner range. Leaving the aegis isn't needed.
Assassins seem to treat all stations in the same way as main stations, that's the bug/illogical behaviour.
Yes, now I've seen the same for a normal hermit as well. Assassin identified by the comms messages.
warning sound if a missile is inbound: Missile warning