In case someone was wondering why in the world someone said we should add a day to the second month of the year...
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.
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.
> How would that have worked anyway, did they have more days per month?
The way I've heard, they just simply didn't track the date during the winter.
Note that some sources suggest that February might still have been the last month, placed after December and before January.
It's fair to say January was the first month of the Roman calendar; despite it having formerly been March.
(You do see "deca" used as a prefix, "a" included, but that doesn't come from Latin.)