The only time they start the day you buy them is when you are standing in Florida at a park ticket booth, Guest Relations location, mall shop location or at the airport.
Any other means of purchasing them (mail, web site, phone) will generate one of two things: your choice of a voucher mailed to you that needs to be exchanged for the activated AP at WDW or a will call order that can be picked up at Guest Relations when you get there. In either of these cases, the year starts the day you exchange voucher/pick up will call.