Generally, that is, not necessarily related to your particular case if there are indeed problems, it does mean that reading skills still rule:
June’s ranked rewards will be based on your highest ladder rank across Standard, Wild, Classic, or Twist.
Just tested it — it appears as a locked (?) chest, but have you tried clicking on it? In my case, it shows all the rewards earned in Classic exclusively, up till Legend.
Does it?
How could you have reached D5 without getting that card back already, unless you specifically have been afflicted by some strange bug? Have you checked it in your collection?
PS That’s right, you don’t have to wait until the end of the month to get a seasonal card back: 5 wins, and it’s ‘yours’ (well, sort of… you don’t actually own anything in this game, all could dissapear like a ‘poof!’) immediately.