That's a big clue right there. They didn't follow the star. If you read other passages in the Gospels you'll see that this star was "in the East," which would have been in the wrong direction if they were traveling westward.
They also wouldn't need directions to Jerusalem -- or even from Jerusalem to Bethlehem (a distance of only a few miles). Anyone traveling in those days would have known how to get to a major destination like Jerusalem.
The "star" was almost certainly only there to tell them WHEN to depart from their homeland and make their way to Jerusalem.
The translation of “we have seen his star in the east” when translated fully means “we of the east have seen his star and have come to worship”. Meaning the magi travelled westward from the East.
That’s why you have a song line in “We three kings” that goes...”westward leading still proceeding following yonder star”
I don’t think they were following the star per se. The star was in a static position in a y axis position relative to the constant movements of other heavenly bodies as the Earth turned about its axis at night. The star stayed in that position though it’s apparent x axis position rose to overhead as the Magi came closer to israel.
Don’t forget what the Bible says..when the Magi left Herod...they rejoiced as the Star appeared before them and came to overhead as the found the home of Jesus.(who was two years old at the time...which tells you how long the magi had been watching this star and why Herod killed all the males in this region that were 2 years and under) This was no ordinary celestial object. It was the Magis burning bush! God even spoke to them in a dream not to go back to Herod. Not a regular star!