To be honest I’m uncertain what exactly is supposed to trigger the Shadowy Assassins to start attacking Southshore, however I’ve completed Dark Council, Syndicate Assassins, Noble Deaths, Foreboding Plans, Crushridge Bounty, Costly Menace, and Soothing Turtle Bisque. I’ve also hung around town for hours while working on other things IRL to see if anybody else triggered the event and I haven’t seen any sign of them.
Edit: I’m on Westfall if that matters
Sat in Southshore for hours. Finally at roughly 8:03 realm time (realm == Bloodsail Buccaneers) I spotted a couple of Shadowy Assassins, however the guards had already killed them before I was able to tag any. Ran behind the town hall next to the trees at coords (46, 59), found a few of them stealthed, killed them to get the Assassin’s Contract quest item. Also of note I think there is supposed to be a town crier that /yells when this event is supposed to start. I never saw the /yell or the crier NPC. I hope this information can be of use.