My experience: I ordered about 12:30pm on the Monday they became available, for our June 8th arrival. Couldn't get anything to go through until then. Received an emailed receipt. Did not pay attention to holds on my card. Kept hearing about everyone getting shipping notifications so I figured mine might get cancelled, but they showed up correctly on the website. Never, ever received a shipping email, however on my USPS Informed Delivery, a shipment from Disney Parks showed up on the Saturday after the roll out Monday.
I wasn't sure if it was that order or an MB order I had placed through the app (I ordered an Independence Day themed one that was on sale for $15 for our July trip because I wasn't sure if the premium bands with reservation would be back in time; btw I still haven't received that one). It was actually under the app, under Shop Merchandise, that I was able to see my MB order and it still said processing, but so did my Independence Day one...so I still had no idea which band(s) were coming.
Finally, I looked under My Magic Bands and Cards and saw the premium ones I had ordered on Monday so I assumed those were the ones shipped. Suppose to arrive this past Friday, even arrived in Atlanta by Wednesday, but then went to SC for a day before coming back to Atlanta, so I received them on Saturday...all correct. The actual charge went through my account on May 30th, the Thursday before they arrived.
BTW, I had declined them to wait for the option to roll out, then edited them that day. Recently I went to decline my July ones because my order date was upcoming and I don't want any plain color ones - I'll edit again if the premium bands come back - and the option wasn't available anymore that I saw. So I chatted with tech support and they did verify that that option is not available anymore on the website. They took care of it for me though.