The cover that is slid into place looks like it is to contain fragments if a defect allows the turbine wheel to rupture at high speed. The wheel remains attached to the machine and there is a position sensor in the machine. The screen shows a diagram to the operator where to remove material.

OK - the cover is to prevent the turbo compressor wheel from circulating air and therefore from taking power to drive the turbine at speed.

In the instruction video on the maker website they have some tool that appears to mark the turbine, but it's quick and not detailed.

I don't see how, but the endcap/cover seems to monitor the orientation and can tell where, relative to that mark, the material needs to be removed.

Not sure if I understand the question, but if I do, rotor dynamic balancing theory and technology has been around for probably at least 100 years, and is basically the same whether a turbocharger shaft, a crankshaft, or the wheels for your car that your local tire installer balances for you.

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz

I kind of skimmed thru the video.
It is hard to see for sure, but a dark, light, or shiny reference for a photocell is probably added to the TC.

Like :45 here -
https://www.youtube.com/watch?v=SJ57d8DnJ68