Your first video is correct. Once the axle nut is tightened down, the speedo drive becomes one with the axle. It is part of the "spacer stack" that runs thru the hub.
The second video presents a problem. Once the axle is clamped in the lower legs, the speedo drive should be locked in place, as the axle is locked in place. That is why you have to make sure the drive is pointing back and level as when the axle clamps are tightened it cannot move.
Or at least its not supposed to.