I didn't appreciate until recently that the calendar we live by today was personally designed by Julius Caesar. Like not by some forgotten technocrats incidentally during his time, but Julius Caesar himself as a subject matter expert, as a side-project. With consultation, certainly, but by his initiative, from long-standing engagement with the problem in one of his early jobs from long before he was a main character…
And in that calender, February is the last month, which makes it the logical month for adjusting leap years.
EDIT: Because there's a lot of confusion in several replies I thought I'd clarify: February was the second month in Julius Caesar's calendar. Romans in the Republic describe the month as being at some point the last month in the calendar, but we don't have any direct record of that. That's what I mean when I refer to it as a legend: it's a story that later Romans tell about their distant past. It is probably accurate but the sources are too far removed from the actual event to be treated as primary sources.
This is true of Roman history in general: any story that dates back to the kings should be treated as a legend that Romans told about their past. It may have elements of the truth, but shouldn't be taken as firm fact. This particular legend has a lot of evidence going for it, but that doesn't make it inaccurate to refer to it as a legend.