When I have made reservations online, with Tiffany TC, they e-mailed me the confirmation. The last time I made ressies with them was earlier this year.
I would allow 1-3 days, and you should get a confirmation e-mail sent back to you. If by chance you dont get on, e-mail them to confirm it. They are usually really good about getting back to you. I have changed ours twice since setting it up since we keep deciding to stay a little longer, and they always get right back to me.