I may have a solution or at least this worked for me. I too was having the issue that all my 4K movies were showing the HD tag in the info bar while playing them. The following corrected this for me.
On the Apple TV, in settings/Apps/iTunes Films & TV Programmes/Quick Start, I had Quick Start set to off to allow movies to buffer ahead. When I turned Quick Start to on the HD tag no longer appeared in the info bar while playing movies. It has now been replaced with the 4K HDR or Dolby Vision tag and the difference in picture quality was immediately noticeable. I have switched the quick start setting on and off many times now to confirm this was the issue and it does in fact remove and add the HD tag. So it does seem that when the HD tag does appear you are only getting the 1080p version of the movie.
This method will hopefully help everyone else with this issue and allow you to get the proper 4K HDR/Dolby Vision version and not just the 1080p version.