A quick question about exhaust and the dmg debuff

Hey,

I just need quick confirmation whether or not exhaust also applies the dmg debuff when you cast it on a champ AFTER they have fired a travelling or dmg over time skill.

For example: 1) does exhaust reduce the dmg of ziggs ult when you cast it on ziggs while his bomb is already/still underway? 2) does exhaust reduce the dmg of a teemo mushroom that is miles away?

My guess is that it does. I'd like some affirmation about that though.

Cheers