Hmmmm- If you have back pain you are not pulling in your stomach tight enough (also known as belly button to spine, setting your abs, engaging your abs). Pilates are designed to work the core- abs and back. Your back is probably is trying to overcompensate for the weak stomach muscles.
This takes a lot of practice- it is hard to keep your abs flat when you are working them- and now that I think of it this is probably where the workout tapes fail! An instructor would catch poor form.
Anyways a couple of hints that I have:
A) maybe this is dumb - but are you trying to do the advanced or intermediate level excercises without mastering the beginner level?
B) ok- barring that. Try to focus on pulling the abs in flat- which will support the back. Do this before starting the excercise. I like to think of it as a big kegel. Make sure the ribs are not wide like you are taking a big breath but 'pointing towards' your spine. So your tummy is tight from the belly button down and your ribs are closed- now start the excercise. It is a hard concept but once you get it you will start doing it all the time!
c) Don't let your back arch off the ground. keep it pressed hard into the ground- using your abs. modify the excercise it you find it happening
d)if your tailbone hurts- is it the rolling excercises? maybe you are holding yourself too straight- or a part of the back is not flexible- try skipping those until you have more flexibility.
Let me know if I can help!