This information really needs to be on the wiki. This is the only place I was able to find it. I wasted a bunch of time running around not doing quests because I thought it was time based.
Also, whether advancing a quest triggers a turn is inconsistent. I was repeating a quest action (due to unrelated reasons) that caused a turn to trigger, only the third time it didn't. The turn triggered after the next advancement in the quest. The fourth time repeating, the turn triggered on the initial quest advancement just as the first two times. I'm unsure if this is a bug or if there are other factors involved.
Additionally, the results of the turn (income, events) were different every time. This is not surprising, just notable.