Huh. I knew about the problem (that’s why I used October as my example, rather than, say, February), but I was mistaken as to the cause. The way I had always heard it told, September–December don’t match their current place in the year because of the addition of July and August. But I just looked it up and it seems you’re right. Those months are merely renamings of Quintilis and Sextilis, and the numbering issue comes from moving the start of the year from March to January.