Charles Ellicott Commentary Matthew 2:9

"And they, having heard the king, went their way; and lo, the star, which they saw in the east, went before them, till it came and stood over where the young child was." — Matthew 2:9 (ASV)

Which they saw... — The words seem to imply that they started in the evening and, as they did so, saw the star in the direction of Bethlehem. In popular language, it served to guide them and so led them on.

We need not suppose that they found the child they sought in the "manger" described by Luke. There had been time for the crowds gathered by the census to disperse, and Joseph and Mary may have found a house in which they could lodge. The expectations that connected Bethlehem with the coming of the Christ might naturally have led them to remain there for a time.