I think there are 2 types of immunity. One is what u get with Roshi, or Kushina Red that is immunity to debuffs which is gained every round. So you cant cc them past one round. And the other is what u get with Edo minato or Itachi ssn, they are immune to all debuffs. Which means they can be cc using suppress immunity + cc skills which last more than one round. This should be mentioned here.

You were right. Its the same type of immunity. I had this misunderstanding because i saw the fire main cc skill + edo itachi sleep + madara barrier effect on my edo minato. I saw him sleep for 2 rounds. And simply assumed that "immune to all debuff" is different and can be controlled. I tried it today with kushina and she also got controlled. I can only conclude that it has to do with the chakra not being above 40 at the end of r1 that causes them to not regain their immunity but I can't confirm, that, that's what causing it. It might be the madara barrier itself.