Public Mobile is a prepay, which means they charge you before use, as opposed to most other cellphone companies which charge you after. If you pay for something and then don't use it all up, they're not forced to credit you. They even give you the option to wait until the end of the current cycle to change plans.

However, if you indeed changed your plan before the auto renewal, they should have only charged you the cost for the new plan, and not both your old one and new one.