It is important that lead officials take note as to which side of the basket line the ball comes into front court. If the ball comes to the front court across the basket line on the weak side, with some energy behind it, the lead should default to that side of the floor immediately and begin the front court possession there.
The reason for this is that teams can get the ball to the low blocks so quickly that officiating crews want to be sure the lead is there to cover the play. If lead officials wait too long to rotate they may find themselves on the wrong side of the paint.
This mechanic requires that the center official accepts the play early in front court so the lead can rotate.
In the clip below the ball becomes live strong side in the backcourt but then quickly enters the front court on the weak side. The center accepts the play and the lead defaults to that side of the court just in time to see a low block play.