When you choose the cortex bomb, your operative will die more easily while incapacitated, I believe it says so in the skill's description.
But it seems that when I switch back to engineer, the engineer will also die easily even though he hasn't got the cortex bomb ability.
Is this a glitch or just something I am telling myself?

I'm not talking about when the character gets curb stomped, I'm talking about how easily my non-operative characters die irrevocably from shooting.

It doesn't say anywhere in the abilities description that you'll die more easily. Are you playing on a harder difficulty?

The OP is completely confused.

cortex doesnt say that , u can find that at : downed fire ( universal abilities )

Cortex Bomb doesn't affect your incap health at all.

Regardless, incap health is very low. 6-7 shots with a CARB-9 will kill an incapped player.