Were the Magi believers?

If so, then why were the Magi still labelled that way? Why call a believer a member of the pagan Zoroastrian religion? Or am I missing something here? And by believers, I meant how the Magi believed in Yahweh BEFORE they saw the star of Bethlehem and arrived to baby Jesus's house. > "After Jesus was born in Bethlehem in Judea, during the time of King Herod, Magi from the east came to Jerusalem and asked, “Where is the one who has been born king of the Jews? We saw his star when it rose and have come to worship him.” When King Herod heard this he was disturbed, and all Jerusalem with him. When he had called together all the people’s chief priests and teachers of the law, he asked them where the Messiah was to be born. “In Bethlehem in Judea,” they replied, “for this is what the prophet has written: “‘But you, Bethlehem, in the land of Judah, are by no means least among the rulers of Judah; for out of you will come a ruler who will shepherd my people Israel."-**Matthew 2:1-6.**