There are several elements in answering this, including the fact that the star was a sign in heaven, apparently a normal "star" that rose and set just like any other star, and that the star must have been to the west (not the east) of the wise men, who as you note were themselves in the East. (That was where they were when they saw the star—in the East.) What the part about the star going before them and standing over Jesus' house means, I have no idea.
But in any case, the most relevant part would be that this would have taken place well after Jesus' birth, probably when he was at least a year or two old. By the time the wise men met Jesus, the sign to the Nephites was long past, a fairly recent historical event rather than a current concern.