Hi Andreasc,
When you dig a tree up, you'll get some set back ! Whatever cares you give to it, but that's not a big issue.
On the first video: when the hell did he water the tree ? the dirt? That's a big mistake from that guy. The roots need wet soil to have better contact with soil.
He adds mulch, but then he no longer can check on the dirt, to see if it settles leaving roots in the air. - That could happen after a good Spring rain.
I wouldn't let the roots dry.
when I move a tree, I plant it asap - in the same hour, the tree is in its new spot.
You need to put dirt over the roots, and water the area. The water will take the dirt to the air pockets that might be located under the root-mass.
Add more soil, and water again; Repeat every other day, until you see that the dirt is no longer disappearing under the tree. If roots get up in the air, add more soil on top.
Water will help the dirt in settling and making contact between the roots and the dirt.
At that point, if you leave air-pockets, those can get the roots to dry and rot.
Then during the following (one or two) year(s), you'll need to water that tree much more, or you'll get a huge setback, or you could even kill the tree .
What often happens, is that the moved tree will bud out, and people think that they are safe and stop watering. What they get to see then, is that the tree all of a sudden crumbles, because the roots can't find all the needed water for all the canopy. The problem being, that when the tree starts to crumble, you'll be almost too late ...
so the key is leaving enough roots (on both videos, they are good at that), and watering during the next seasons.
Good luck !
PS: Damned, now that's a Panaché tree. But funny here, the bark turns Grey on the trunk ... On his tree, the bark on the trunk is still green ...