When I went there I ordered a large plain, which was a typical upside down square pizza. Cheese was under the sauce as in the attached pic. I grew up outside of philly, and to us, a tomato pie is anything that doesn't have cheese, and is just sauce on a crust. We also have "bakery pizza" which is a thick ready dough with what appears to be tomato paste on it, and might have some parmesan sprinkled on it lightly. The Santuccis I've been to is just like Picas, except for the crisper crust.
Thanks for providing the photo of Santuccis square pizza. It looks very good. Lol, about a tomato pie outside of Philly being anything that doesn't have cheese. I made what I call a tomato pie and it does have sauce and cheese.