The tile displacement occurs to other units as well. But only if you press another unit immediately (like for 0.5 secs) while the previous unit is animating to its designated spot.
A guy once said, "If you love a flower, don't pick it up. Because if you pick it up, it dies and it ceases to be what you love. So if you love a flower, let it be. Love is not about possession. Love is about appreciation."