(which should automatically mark it as adult)
That's not how this works. I believe you get a reminder when selecting such tags. But you need to click a check box to mark it as adult. It is not fully automatic.
You can have the tag adult and not be marked as nsfw. It is not the same. One is a tag, the other is meta information.
The game in question has a nsfw warning/age verification box. It was updated around the time you made this post.