Alright so 
ults me, then 
eats me. I assume I'm going to get saved, but when I got spat out it looked like WW was still damaging me.
So he can not only cc u, but keep you steadily damaged while ur inside of him before spitting u out into his team?
That's normal. It's a channel and WW himself wasn't interrupted so you were still under Infinite Duress' effects.
Being eating makes you untargetable, not invulnerable. Once Warwick ults you, the DoT is already on you and becoming untargetable doesn't negate damage from DoTs.
You can't stop the damage portion of Infinite Duress unless you hard cc WW, you can only stop the cc. If Tahm eats you but brand burned you, you will still die, same thing here.
