League of Legends damage modifiers while channeling

So I tried this stuff out a bit and I came to the following conclusion:

Every damage modification is applied Instantly

This means that the damage of a spell/dot/projectile is applied for the exact duration of the damage buff or debuff. The damage of an Ashe arrow for example is reduced only if she is exhausted on its impact. Dots work similar (I tried this with teemo shrooms): When someone walks into your shroom and you buy an item with ability power during the DOT time the dot will become stronger as soon as you have the item in your inventory (Same goes for leveling up a skill. I had this with malzahar e before). The dot damage is lowered for the duration of the exhaust on teemo and is also applied immediately. This also means that if an ezreal fires an ult for example it won't help if you exhaust him while he's channeling if the ult hits 4 seconds later.

TL;DR
Exhaust reduces damage while it's on the enemy. Not before and not after.

Jutschge has the right answer but just to make a more general one.

Damage on abilities/auto attacks are calculated at the time the damage is taken, not when it is cast.

Channeling abilities are damage over time not continuous as they look so every tick of damage will go through all the math required to determine how much damage it will do (eg armor/mr, debuffs, pen etc).

Ex1) Jinx shoots her ult across the map, but you exhaust her before it hits the target, the damage will be reduced by 30%

Ex2) Lucian is channeling the culling(his ult), and you exhaust mid channel, all subsequent shots will have 30% reduced damage. (Note: the amount of shots based on attack speed will not change as this is calculated at the time of cast)