It is the damage the champion that is exhausted IS DOING AS THEY ARE EXHAUSTED.
So, for instance, if you were to exhaust a Zed who all-in'd your ADC, it would be better to exhaust a bit BEFORE DEATH MARK POPS. This would REDUCE THE DEATH MARK DAMAGE, since the champion is dealing reduced damage.
Think of it as someone going to punch you, and right before it hits, you apply a large layer of bubble wrap around object hitting you for a few seconds.
Softening the blow.
So, yes, the damage from Equalizer would be reduced if you were to exhaust Rumble as the Equalizer was on the ground. However, if you exhaust him as he casts it and it lands, that would have little to no effect on reducing the damage taken, as exhaust is a very short spell. The Equalizer would deal full damage after the exhaust wore off.