The game will distinguish between Vanilla mods and Definitive Edition mods. So be sure to download the correct version of a mod, according to the game version you want to play in.
So just to clarify in my mind how this will work ... I take it the game uses that new workshop tag to identify whether a mod belongs to classic or DE? If so, when a mod is compatible with both apart from any changes, does an author need to upload it twice, once with the new tag and once without? Can an author simply add the tag to an existing workshop item without re-uploading or is the tag somehow automatically applied by the DE version of the editor when uploading.
Sorry if this is all obvious and I'm dense.