That is right. MP3Tag is no photo-viewer and takes the picture like it is. The orientation flag is a feature for viewers to correct only the view of the pictures, not the pictures itself.
What really happens with rotating and viewing depends of the software you use and whether you strip the metadata before rotating or not.
There is image-software that writes a new orientation flag with rotating and there is imaging software that doesn't change the orientation flag. There even is imaging software that writes a new orientation flag with rotating even if there are no exif-dates before because you stripped all metadata (like Windows).
You have to examine and look if there is the orientation flag again after rotating with your software
There also is software (like Irfanview with it's lossless jpg-rotation features) that rotates pictures according to the orientation flag, not only for viewing but really changing the pictures.
If there is any music-player that displays the cover according to an exif-orientation-flag is beyond my knowledge.
Maybe your phone's software has changed?
You mean rotate the photo in the embedding-process according to an orientation flag? I think that goes too far. Mp3Tag is not an imaging software.
Anyway: I never thought before that people shoot pictures with their camera to create covers.