Turning focaccia upside down before topping
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.