It very clearly states that since 1918 the american spelling has been ‘extrovert’. That has nothing to do with whether the A or O is correct, only that O is more common in American English.
It also says she changed the definition, that’s the nature of language, it evolves. That can be through a colloquialism, a hard change (as this seems to be), or many other reasons.
I am not arguing whether it is correct or not, I am simply saying it is different.