I have consulted my global payments expert and here is what I've learned:
Your unpaid USD earnings from May will be issued to you at the end of June, provided you have exceeded the threshold amount. Any monthly earnings accrued during June will be finalised in your local currency and posted to your payment history page in the first week of July as per usual.
For those of you who are eligible to migrate to local currency reports but haven't yet, please note that this won't affect the timing of your payments. If you migrate your account today, your June earnings will be converted to your local currency between July 12th and 15th, and if you've exceeded the payment threshold, you'll be issued a payment for those earnings at the end of July.