This is the support page for Roman Dates : convert any date into roman numerals.
The dates will either appear as Day-Month-Year or Month-Day-Year. This is determined automatically from your regional settings on the iPhone. If you have your phone set to US English then the dates will appear as Month-Day-Year.
When you change your regional settings, the date picker automatically changes, but the roman numerals doesn’t change. Make sure that you change the numbers on the date picker so that the dates appear correctly.
If you want to convert Roman Numerals, then the Roman Nums : Converter app is probably what you are looking for.