You should always make your back cut level and about 1-2" above the level plane of the face cut (notch) in order to leave a surface that the tipping trunk can push against to prevent it from sliding back over the stump towards the sawyer. As the tree is falling, the butt is getting pushed by the top in the opposite direction the top is falling in. If the back cut slants down towards the face cut instead being slightly above it, you've created a ramp for the butt to slide up towards yourself as the tree tips over. This isn't quite the same as a barberchair though because the wood hasn't actually split or broken. As I understand it, a barber chair is when the trunk actually splits along the grain sending the part above the back cut towards the sawyer, usually due to a heavy lean and/or brittle wood. The effect is the same though, which is pretty bad - people and trees are about the same relative size as baseballs and bats.
I think the Fundamentals of General Tree Work should be required reading, especially the section on falling techniques. This was my employee training manual when I first got started, and I had to pass a written test to prove I had read it (all 500 pages) before I could even show up on a job site. I've never seen another source of info on felling techniques that was 1/2 as good.