My Temple Patriarch just started the main quest and ran the first errand for the Fighters Guild guy, and random sleepers in Balmora are already thanking me for saving them. Huh? I haven't even gotten a strange dream yet nor any sick rambling from sleepers - the first time they talk to me they already thank me. Why is that?

One of the Temple quests sent you to Hassour. By killing Dagoth Favon there you saved a number of Sleepers already.

I see. Thank you. I was worried that I've broken the main quest somehow. Does it mean, this character won't experience the dreams and sick rambling of other sleepers? Kind of makes sense, come think of it - him being Temple Patriarch and all.

No, he'll experience the dreams as intended and sleepers will still talk to you.
There are many other sleepers out there, waiting for you.