I don't know how smart you are, but you seem to be a very perceptive man.I believe the stomping also releases interdigital scent so the other deer can locate/follow. I am not a biologist but I did stay in a holiday inn express once. Have had many a deer stomp at me. Have had my wife stomp too but pretty sure the intended message was different.
Like you, I have also seen my wife stomp.
Usually, at that point, it is best for me to flip my tail up and run.