The shape that is created on the initial map processing is not changed when doing the manual referencing. X Y adjustments are made to make it line up. These X Y adjustments have a small amount of stretching/pinching that can occur to the image to get things to line up well. This is called 'Thin plate spline' adjustment.
For the height (Z axis) only a fixed offset is added or subtracted to account for gross differences. The total error at all of the points is minimized but is likely not going to be zero.
It is important to start with the best model you can get by using lots of overlap, 80% or so, and include a Ground Offset image with your uploaded data set if you can.