They are supposed to send you a confirmation after you make any change to your ressie, including making a payment. Notice, I said "should". They don't always send them. In fact, I did not get a confirmation of my final payment last August.
One newer feature of their website (disneyworld.com) is that you can view your ressie online, even if you made it via telephone. Go there and click on the "my disney vacation" link to view it.
I have yet to receive my initial confirmation from a ressie I made in Dec. It is listed online and I have called to confirm, but still no written ressie.
Duds