Set SRS button in the Georeference tab in ArcGIS Pro does not set the coordinate system of the map as described in the ArcGIS Pro: Georeferencing tools web help page.
The software is working as expected in the video. It is simply a misunderstanding of what the intent of the button is for. When georeferencing (think back to Desktop 10.5) you had to manually set the Data Frame Spatial Reference. Many users complained that a more intuitive system should be in place.
So the design of the button is as follows:
(i) if there is no spatial reference on the raster you are georefernencing, then use the current map frame as default but also bring up a dialog to let the user choose a different one.
(ii) if the raster you are georeferencing already has a spatial reference, automatically populate it as the Map SRS. If the rater already has a spatial reference that spatial reference must be used while georeferencing.