The reason that the image “appears” to shift has to do with the fisheye effect of the lid camera. For that reason, you pretty much HAVE to keep all of the information on engraving in the same file, because while it can be hit-or-miss by a bit as to where a file gets placed, the relationship between parts of a file are sacrosanct.
So if you set the backside engraving to be a different color, then align everything perfectly inside the design file, along with the cut line, everything works out perfectly. The cut will land somewhere close to where you dropped it, but the engraving is always going to land exactly right in relation to the cut. (Just like it says in the tutorial.)
Your two files are not exactly the same. The one that says Tapped does not contain a cut line, it’s just the score line. So that enclosed engrave is not going to land in the same place as the enclosed engrave that also has a cut line. (That introduces error when you are trying to place cuts right up against the edge of the printable area.)
Okay, so if you do what is in the tutorial, you will resolve one problem.
The other thing you likely need to do is run the Improved Calibration program first. It’s brand new, just came out, and it dramatically improves visual alignment for those who try to do things by eyeballing it on the screen. It’s still not going to be 100% perfect at the edges of the bed because of slight fisheye stretch, but you can also use Set Focus to get a really good picture anywhere on the bed. So if you are trying to do something out in the corners, use Set Focus to correct the view and you’ll get much better results at that spot. 