Yeah, that sounds like a mistake by the tweeter. As far as I know there have always been 12 months, but the start of the year got moved from March to January at some point.
Yeah, what I'd learned as a kid was that Julius and Augustus inserted themselves in the middle to turn it from 10 to 12 months, which is why the latter months are named wrong, but comments up above are saying they just renamed months.
That’s confusing a few separate things. There was (supposedly; we only know about it from late Republic writers) a system with ten months, _then_ a system with 12 months where the year started in March (so the numbering made sense), then at some point the year switched to starting in January, then Julius Caesar’s system, also with 12 months.
Later on (during Augustus’s rule, I think), Quintilis and Sextilis became July and August, but by that time they were _already_ confusingly named.