I'm on PS3 but seeing as there's no answered yet i might as well, i've never had a random encounter with the Morag Tong and except for some small things in Raven Rock (like the Mazte quest) that questline was what i did first on the island so i was there for plenty of time after.
I have, but for me they left a note behind mentioning I was "a freelance assasin working for the Dark Brotherhood" behind which instructed them to kill me. I had the encounter twice on that path above Raven Rock overlooking the temple.
It seems to show up roughly when the dragon respawns.
184.108.40.206 wrote: I just got a random attack after I've finished that quest just west of Tel Mythril next to the deathbrand armor
Have you joined the Dark Brotherhood? if so, they will attack you with a letter on them saying that they can kill you because you work with the D.B, if you completed the Deathbrand quest then you should be able to kill them easily or have enough armor to run away.
you must be a member of the Dark Brotherhood, since the Morag Tong and The Dark Brotherhood are rival guilds, i'm not sure of this but if you destroy the Dark Brotherhood, is most likely that they won't attack you; all the attacks i have encountered they always carry a writ of execution, relating my alliance with The Dark Brotherhood, even if you kill them in Served Cold, the random attacks are more related with your relation with The Dark Brotherhood