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.
The wise men were spoken to, by God himself (not, as stated, by an angel) in a dream :


  And being warned of God in a dream that they should not return to Herod, they departed into their own country another way. [Matthew 2:12, KJV.]


If God spoke to them - and they clearly heard him, since they took note of it - then, being in communication with God (himself, not an angel), they thus believed in God.

And having gone on a journey which took two years to complete (the time which Herod took note of, in his calculation as to which children to slaughter) and which would necessitate another two years in which to get home, surely they did so not to merely visit the entry into the world of just another human being (not to belittle such events, but really, four years !) they came for a serious purpose.


  Then Herod, when he saw that he was mocked of the wise men, was exceeding wroth, and sent forth, and slew all the children that were in Bethlehem, and in all the coasts thereof, from two years old and under, according to the time which he had diligently enquired of the wise men. [Matthew 2:16, KJV.]


They were wise. Wiser, in context, than the Jews who had received so much divine revelation, it appears. And is probably the whole point of Matthew recording the matter, in his particular account and with his particular aspect of Christ in mind, to highlight this devotion from outside of Israel as a testimony to unbelieving Israel.

Yes, I would say these men were believers and remarkably and devoted so, it appears.


  When they saw the star, they rejoiced with exceeding great joy. And when they were come into the house, they saw the young child with Mary his mother, and fell down, and worshipped him: [Matthew 2:11, KJV.]