First, I don't think we can say for certain that the priest told Alexander that we was the son of Zeus, or that Alexander himself fully embraced such a claim. But in any event, Plutarch's account states:

But Alexander, in a letter to his mother, tells her there were some secret answers, which at his return he would communicate to her only. Others say that the priest, desirous as a piece of courtesy to address him in Greek, "O Paidion," by a slip in pronunciation ended with the s instead of the n, and said "O Paidios," which mistake Alexander was well enough pleased with, and it went for current that the oracle had called him so.

Paidion = my child

Paidios = child of Zeus

So Plutarch's unnamed sources seemed to think that the priest spoke Greek, albeit without a complete mastery.