No. I applied for the no-fee card last year through a referral that got me the $200 gift card. That gift card was received, loaded to the gift card site, and spent many months ago.
I just applied and was approved for the Disney Premier card earlier this month (around the 6th, I think). I received the card a few days later, met the spend in one day (purchased $500 Disney gift card), and my statement closed yesterday.
This recent card is a "Disney Premier" according to the offer I was responding to when I applied, the card itself (says "Premier" under "Disney" on the front), and the literature that came with the card. It's a completely different account number than my no-fee card from last year (which is still open). I have also SMed Chase to make sure I will get the $200 gift card, and they assured me that I would, and referred to the card as my "Disney Premier" Visa.
On my Chase accounts page, the card is called a "Disney Rewards" Visa, and this is what is printed on the statement pdf as well. I'm not sure why that is, probably just a peculiarity that means nothing.
At this point, I'm thinking they just held off on posting the AF until the next statement. And after thinking it through and talking to some other folks, I'm not going to downgrade or cancel the card. I'll pay the fee (assuming they ever post it) and keep it through the year. I've got 10 Disney Rewards points on it now, so maybe I can get 10 more out of it over the year and then redeem my card and cancel/downgrade before the AF rolls around again.