Some Figure accounts have an advanced shipping option which allows for a more customized shipping setup on individual states.

If you go to the Settings>Shipping States & Taxes page, you will see a list of states. 

There are two different Figure setups that allow you to modify the shipping methods viewed per state:

On the far right column is an Edit button for each state. 

OR

Click the name of the state.

Both options will make your shipping methods appear in a window.

Most likely, the shipping method(s) that are showing $0 in the admin cart will not be selected as a shipping option for this state. Once you select the box and affix a Zone to that method, orders from that state will have access to that shipping method and it will be populated with the correct cost that you have setup on the Settings>Shipping Rates pages.

If you have customers trying to buy online and a shipping method is not selected for a particular state, that method will not appear in their cart as an option.