The fee is charged by a secure 3rd party payment processor, and it is charged to cover the cost of interchange fees. Interchange fees are what is charged by credit card companies and banks for the ability to use credit cards. For example, if you pay with a credit card issued by Acme Community Bank, a percentage of the fee goes to Acme Community Bank, a portion goes to the card network (Visa, MasterCard, Discover, etc), and a portion goes to the payment processor.
Whereas private businesses can increase the prices they charge to "absorb" the cost of interchange fees, local government agencies can not. Because of that, the processing fee must be paid by the customer to the payment processor. No part of the processing fee goes to or is kept by the Manatee County Tax Collector.