Crit+Hatred/added fire damage interaction

So i thought about the hatred aura and the added fire damage support skill and how they would interact with crit.

So they are based on the physical damage dealt. let us say we would deal 100 damage and have 200 crit multiplier and the hatred aura with 30% physical added as cold (round values for easy calculating^^)

a normal hit woukd do 100 physical + 30 cold. simple
Now we would crit. so we would do 200 physical damage. Now the interesting part: since the elemental is based on physical damage we in theory would first increase our cold damage to 60, and then you should actually crit with that 60 damage actually doing 120 cold damage which is insane.

I already noticed the whole screen exploding into tiny shards when critting with ethereal knives before but i cant really say with 100% certainty that it is that way since i until now built a shadow without crit multiplier increase (stfu all potential haters: it works :D)

Even if it would not work: Hatred is a really cool skill no matter that everybody says it is worse than the other damage auras. Freeze really gives you a lot of defense which helps a lot if you play shadow which by default ist the most fragile of them all :)

if a crit makes physical damage 200 and you have 30% added cold via hatred, then it is 60 cold.
it'll be easier to look at it this way. your base was 100 and the cold is 30. now multiply those values by the crit, because crits affect every part of a damage while keeping it the same. you accidentally doubled the ice, which isn't true and you can even look on status page usually.

But this would mean that its damage isnt actually based on the damage the hit does!

See. When you have an aura that does 30 damage and you crit with 200% it deals 60 damage.

But if it is %-based on physical which gets amplified by 200% the cold portion in theory WOULD NOT CRIT if your theory would be true.
Sure it is possible, maybe aura damage is uncrittable or not actually based on physical...but idk..
i would like to know the underlying mechanics

aura boosts your damage. auras do not hit things. attacks or spells do.
a crit works on ALL damage of a hit. the hit is physical and has cold damage thanks to hatred aura.