If you downgrade to a plan during an active subscription, you will be charged the new rate on your subscription renewal date.
For example, if a user who has a Premium Membership ($9.99) with a renewal date of August 28th downgrades to a Standard Membership ($4.99) on August 22nd. They would be billed $4.99 on August 28th and the 28th of each month for a Standard Subscription unless changed.