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.’”
Then Herod called the Magi secretly and found out from them the exact time the star had appeared. He sent them to Bethlehem and said, “Go and search carefully for the child. As soon as you find him, report to me, so that I too may go and worship him.”
(Matthew 2:1-8)
they didn't follow the star to Bethlehem, but somehow inferred that they should go to Judea. they must not have gleaned such specific information from what they saw in the heavens -- else they would have gone straight to Bethlehem instead of going to the presiding king of the land and making further inquiry with him.
please notice, again, Herod found out the exact time the sign had appeared, and then ordered the death of all male children up to 2 years old. that gives us strong evidence that it had been approximately 2 years between the time the magi saw this, whatever it is, and the time they arrived in Judea.