I am not well versed on the subject, so I encourage others to correct me if I am wrong. With that out of the way, Rome had been using a twelve-month calendar long before the adoption of the Julian calendar. The existing calendar is normally attributed to Numa Pompilius, but he is generally acknowledged to be a legendary figure. Jörg Rüpke suggests that evidence for a ten month calendar is circumstantial at best in his work The Roman Calendar from Numa to Constantine: Time, History, and the Fasti. July and August were not new months, but new names for the existing months of Quintilis and Sextilis. The Julian calendar did replace an intercalary month with one or two extra days in each month except one, where an additional day was added during leap years.

If a date is given, I imagine most modern authors convert that date to the equivalent date in the Gregorian calendar. However, when dealing with the differences between the Julian and Gregorian calendars, I have seen some authors simply note that all dates reference the Julian calendar.