Whether you are configuring the plugin for the first time, or making changes to update your current shipping model, testing these changes can be confusing when you are not seeing any change. WooCommerce actually has its own cache built in to the shipping system to improve efficiency. Shipping is recalculated only when the order changes, or at certain stages during the checkout process. So if you have updated your shipping costs and simply refreshed the cart, your shipping costs may appear to have not changed.
Fortunately, WooCommerce has a settings field built in to help with this. The Debug Mode in your shipping settings will disable this cache and ensure that a new calculation is made with every page load. It will also include a banner at the top of the page stating the shipping zone it selected for the customer. This can also be helpful if options are not showing up, or if the wrong options from a different zone appear.