I was under the impression they were already shipping. The email that told me they were going to start billing on June 1 said they were billing so that they could start shipping them. A least that's how I took it.

Thank you for your preorder of FINAL FANTASY® XIV: Heavensward™. We are pleased to announce that we will soon be preparing your order for shipment. As part of this preparation, we will begin charging for preorders on June 1, 2015 using the payment details that you provided upon checkout.