Nevermaker

Effects that cause you to pay more or less to cast a spell will cause you to pay that much more or less while casting it for its evoke cost, too. That's because they affect the total cost of the spell, not its mana cost.

When you cast a spell by paying its evoke cost, its mana cost doesn't change. You just pay the evoke cost instead.

Whether evoke's sacrifice ability triggers when the creature enters depends on whether the spell's controller chose to pay the evoke cost, not whether they actually paid it (if it was reduced or otherwise altered by another ability, for example).