Since Purge the Wicked is Radiant damage (Holy + Fire), it will be buffed by Twilight Equilibrium. Buffing Purge the Wicked via Twilight Equilibrium causes the entire DoT to be buffed by 15%. If you spread the buffed DoT via Penance, you spread the buffed version of the DoT. Refreshing the DoT without the Twilight Equilibrium buff will overwrite it with a normal, non-buffed version.