Turning focaccia upside down before topping In this video (you don't need to understand Italian ;) this lady lets a focaccia leaven in its own baking tin on a layer of olive oil and then, before topping, turns it upside down.
The tins were covered only with a towel, so the dough did form a bit of crust.

I can imagine that the point of turning can be in order to have the wetter side on top and the drier on the bottom, but what's the advantage in comparison to brushing the dough with olive oil before the rising? I think the point of rising in the dish is lost if you manipulate the dough again, no?
I understand it the same way: the wetter side on top. The Bottom side sucked up the oil while leavening. And by turning the dough she gets also the other side greasy. 

I think the lady just likes to use her hands. As she turns the dough she pushes her finger inside it to spread it.

I actually don't see a different way to do the focaccia as you are supposed to push in with your fingers. She opens the cherry tomatos also by hand because she wants some juice to come out and fall in the small hollows of the dough.