I have both Wasteland 2 and Wasteland 2: Director's Cut. They are separate games with their own achievement lists (although identical to each other).
Espio Idsavant's achievements in Wasteland 2Espio Idsavant's achievements in Wasteland 2: Director's CutWasteland 2: DC does not appear in my overall list of games, just Wasteland 2 does
Espio Idsavant's GamesAlso if I go to My Achievements, no achievements for Wasteland 2: DC are listed, even if the game is selected in the Game filter box.
I've randomly checked a few people who are listed as having the DC version, and it doesn't appear on their game list either.