I have just started learning to use a thumbring, and have a long ways to go before I can call myself proficient, but....I just love it. I hadn't shot all winter, and after about 1/2 hour, was shooting decent groups at 100 feet. I still tend to shoot to far to the right, but that will go away with practice and concentration.
It is indeed strange to shoot off the right side of the bow (and right thumb as I gripped the bow). The rule of thumb (pun not intended) is draw with the fingers at draw, shoot off the finger, and draw with the thumb, shoot off the thumb. As for where to anchor the draw, that is up to the archer, and the ring doesnt care where you anchor.
One other observation - because of the lock you make with your right hand, the top of your hand is facing up toward the sky, whicy faciliates a very long draw. To shoot, you simply open your hand.
When I got the ring (3 Rivers), I also bought the Kay's Thumbring Book, which I highly recommend. She points out that when someone is proficient with the ring, you can shoot of either side of the bow. But until then, stick to the right side. Not having to worry about a shooting glove or a arm brace is nice. The bow torques to the right with the ring, so the string won't scrap your forearm. A perfect release will not cause any torquing.
She also brings up some interesting sociology and history in the book, and different styles of thumb devices from Africa and other places and cultures.
I tried the ring with a flat bow and a "horsebow" and it seems to be fine with both types of bows. Not sure yet about how much wear on the string the ring will cause, but that is part of the learning process.
Dane