The calendar was regularized to include a leap day during the reign of Julius Caesar (hence the name "Julian calendar"), which would have been 45 BC.
The Roman calendar moved to January as the first month of the year in 153 BC, over a hundred years before the leap day was added. The 10-month calendar may not have even existed--we see no contemporary evidence of its existence, only reports of its existence from centuries hence and the change there is attributed to a mythical character.
Btw, the Romans had leap days before Julius Caesar, but they were added ad hoc by the Pontifex Maximus.
Caesar happened to be the Pontifex Maximus (an office you hold for life once elected to), but he wasn't in Rome much to do that job. So after he came back from hanging out with Cleopatra in Egypt he came back and set the calendar on auto-pilot.
Are you saying that while we do see evidence that September, October, November, December were once the 7th, 8th, 9th, and 10th month, we don't see any evidence that the calendar was ever "10 months long"? (How would that have worked anyway, did they have more days per month?)
I don't know if it ever made it to production, and I don't remember exactly why it made sense at the time, but one early hack I did was passing a date in Julian format because there weren't enough bits to pass a full timestamp.
That's correct, the Romans had March as the first month of the year, so leap day was the last day of the year and September, October, November and December were the 7th (sept), 8th (oct), ninth (nov) and 10th (dec) months.
Technically, the leap day (bissextus) was the 24th. (Wikipedia tells me this is because that's when Mercedonius used to be, before the Julian reforms.)
You are right. I should have written: (septem)ber was the 7th month of the year, (octo)ber was the 8th, (novem)ber the ninth, and (decem)ber the tenth!
In case someone was wondering why in the world someone said we should add a day to the second month of the year...