Before you make a melee attack roll, you can choose to spend one use of your channel energy ability as a swift action. If you channel positive energy and you hit an undead creature, that creature takes an amount of additional damage equal to the damage dealt by your channel positive energy ability. If you channel negative energy and you hit a living creature, that creature takes an amount of additional damage equal to the damage dealt by your channel negative energy ability. Your target can make a Will save, as normal, to halve this additional damage. If your attack misses, the channel energy ability is still expended with no effect.
Sorry I meant to say that the feat I'm asking about is Channel Smite. Do you apply your cruelties through your weapon with the feat, similar to conductive weapon?
You would not, because you're not technically using Touch of Corruption (which is the ability that applies the Cruelties). Your Channel Negative Energy ability uses charges of Touch of Corruption as a resource pool, but is otherwise a separate ability and has nothing to do with Cruelties.