Don't think you are supposed to get the assassins, but the thieves, yes, they are supposed to accost you after being Guild Master. IIIRC, if you are wearing Nightingale armor when a thief shows up, they won't demand money from you (but don't quote me on that). It's not immersion-breaking (on the thieves, that is) - thievery is actually supposed to go up. I know that the random night thief in the town of Riften seems to show up alot more the further you progress in the questline.
I'm not sure about the Nightingale armor. My TG character wears it most of the time, and I still get stopped by thieves - but she hasn't been wearing it ALL the time, so I might be wrong there. I only got the option to say I was in the Guild the first time, though. I just assume that the rest of the random thieves are working on their own

(And the random thief in Riften shows up EVERY night, I swear, even though I'm not Guild Master...)