So sorry to hear that you acquired some pain with your low back after doing some of these exercises. However, I would like to ask which particular position causes pain? In normal healthy individuals, there should be no pain when doing these exercises, other than tightness and limited range of motion, unless you are also suffering from a co-existing injury. If there is pain with doing such routine, I advise you to refrain from doing Invincible Core for the mean time.
I also suggest to consult your doctor to check whether you have existing back or spine injury that may be causing the pain.