"After the Reconquista"??? What date is that? Just at random, here is a vulgar Latin text from 922 (near Burgos):
deinde in villa que nuncupant Cavia, que est sita in alfoz de Munno[...]
Believe me, the Reconquista was not yet finished in 922 A.D.
The question posed by this thread has been recently discussed by scholars. You can read
I am a complete, absolute, total ignorant about these issues, but it seems that scholars consider some features of Andalusian Arabic as the source of these "al-" Hispanic words.
Reconquista lasted many centuries, so you can’t fix it at any particular date. It was, however, finished in 1492, as far as I know.