The meaning of
ex in ex-dividend is not "outside".
As originally used in the financial jargon ex-dividend date, ex is used correctly and has the sense "after (in time)". That is, if you buy something ex-dividend, the dividend has already been paid (you're buying after the payment), and so you won't get it. [1] It's sense II in Lewis and Short ( http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%... ) (Note sense II.A.2, which gives us the more vernacular English prefix ex-, as in ex-wife.)
"Outside" is not even one of the many senses of ex in Latin; ex always has a sense related to the core concept of "from". "Outside" is extra.
[1] For some reason, the ex-dividend date is one day before the actual payment, but the idea is still that you're buying after the date of the dividend.