According to Matthew, King Herod secretly asked the wise men when they first saw the special star because he wanted to know more about the baby they were looking for. Herod was pretending to be interested, but he really had other plans because he was worried about losing his crown.
Matthew 2:7: Then Herod, when he had privily called the wise men, enquired of them diligently what time the star appeared.
In Luke 2:16, the shepherds visit Jesus soon after his birth, which contrasts with the timing of the Magi's visit in Matthew 2:7, suggesting different timelines for the events.
Luke 2:16: And they came with haste, and found Mary, and Joseph, and the babe lying in a manger.