If you have a Disney visa card you can book it now. You do not have to wait until you receive any notification from Chase or Disney.
Just call, say you want the Disney Visa free dining, and use your Disney Visa to make the deposit.
You may not be able to do the Disney Visa booking online. Not sure about that one but I think you might have to call.
if you do not have a Disney visa card you will need to wait to book until the offer goes public on May 7.
Next question, currently I have paid for about half of my reservation (resort, tickets, memory maker). Do I need to finish paying it off and then ring Disney to get my reservation re-done? Or should I just ring ASAP when the offer goes public next week? (Trying to avoid too many international phone calls!)
If you already have a package and you are applying the free dining to it, you do not have to have it paid in full, and you had better call them ASAP to be sure you get the resort and dates you want, because there will be a limited number of rooms offered.
Make sure you check the exempted resorts, if you are staying at one you will need to change your resort to get the promotion. Port Orleans (both FQ and POR this time), Art of Animation Little Mermaid section, Grand Floridian Villas (just the villas, not the hotel), All Star Movies, Fort Wilderness campsites and all 3 bedroom villas are excluded.
The only reason you'd need to cancel and rebook is if you have previously booked a room only reservation and not a package.