Actually, if the overarm is over the rest post, it puts the changer into semi-auto mode. The arm returns to the rest post after the record, but the changer does not switch off. This feature was added to V-M changers in the early 1960s, and remained until they stopped making changers.
From the video, I see the automatic shutoff is not working. With the overarm in that position, the changer should shut itself off. It could be the overarm is binding or caught on a wire, keeping it from dropping all the way. I suspect dried grease on the shutoff parts.
The arm should index the way it did because of the wrong way the changer is being used. Since the record was not up on the spindle when the changer was started, the 12" record sensor was not activated by the dropping record, so the changer set down for a 10" record. This is normal operation for a V-M intermix changer. On this model, you can't start a 12" record already on the platter and expect it to work.
So there is nothing wrong with the setdown adjustment, just how the changer is being used. Put the record up on the spindle ledge, put the overarm on it, and try it. It will set correctly on the 12" record because the dropping record hit the sensor.