The grammatical logic is: doisprezece and douasprezece literally mean "two and ten" which leaves the "two" subject to the gender of whatever it relates to. Kind of like "doi si zece baieti". douazece literally means "two tens", meaning that the "two"'s gender relates to "tens" which is feminine, regardless of the context.

There is a logic if you think of 'a douăsprezecea' as the phrase 'two on top of ten', so this 'two' will follow the gender of the noun (in this case feminine, the masculine with the same loguc must be doisprezece). In the case of 'twenty' you say douăzece which literally means "two tens' and since zece (ten) is feminine you have to use'două' and not 'doi'.