Let's suppose I am talking about people in general, but my subject of the talk is 'people', the plural noun. Now, which of the following fit best?
Their heart turns to piety.
Their hearts turn to piety.
Thing to be noted is that I am talking about all of them at a time and of course everyone has 'one' heart. So if they are 100 people, it will make a hundred hearts I am talking about.