The first time he died he was definitely in the demon trap. And on his death you can see your HP go to 0 and your cheat death passive triggers and goes on cooldown.
Second time is definitely also a demon trap since you trigger one about 2 seconds before you die and templar ports to you right then, right to the center of the trap just before it explodes. Since cheat death is on CD you die this time.
I can't say for sure one way or the other on mechanics but it kinda does seem that you do get 50% of the damage even if that damage is overkill. Demon traps do hit hard. One could test how much damage is shared on a reg hero I think.