I don’t think this is a caching issue, it’s more that Event Espresso doesn’t have a way to enforce that type of discount if it’s tied to a specific payment type.
May I ask how is the discount given in the first place? Are they selecting a ticket option or inputing a promo code at checkout? I’m not aware of an option within the payment methods that gives a discount if a specific type of payment is selected at checkout. Maybe that’s something that was custom developed for your website?