I don’t believe UChicago EA is true rolling admissions (not familiar with Tulane). There is an admissions date on which all EA applicants are notified. True rolling admissions means the school makes decisions as applications come in and there is not a separate admissions track which is the case at UChicago, which has 4 (EA, ED1, EDII and RD). I am sure the AO at Princeton can give you a definitive answer. This is not something I would chance getting wrong and getting an authoritative answer is easy.