The Update Billing Address feature works to update the Billing Address fields on the Chargent Order. The Chargent Order will update both the Billing Address field and the Billing Address Line 2 field as well as the City, State/Province, and the Zip Code / Postal Code. Every time a Payment Request is issued from Chargent Anywhere a new Chargent Order is created with the updated billing information.
If you are using Payment Requests from another object other than Chargent Order, the Billing Address is pulled from the Mailing Address of the Contact. Since the Mailing Address on the Contact record is not updated with the Update Billing Address feature, you would need to create a Process in Process Builder to update this field on the Contact Record.