Reference is made to the king of Assyria since the Persians ruled over same area that the Assyrian kings had ruled previously. Darius, even though he was the king of the Persian empire, ruled over the territory that the Assyrian kings had previously ruled over. He was thus also the king of Assyria.
22 And they kept the Feast of Unleavened Bread seven days with joy, for the LORD had made them joyful and had turned the heart of the king of Assyria to them, so that he aided them in the work of the house of God, the God of Israel.