Testing public methods with any testing framework is easy because we have access to the public interface of the test subject. Unfortunately, we don’t have access to the protected and private methods of our test subject. They are hidden to us (the client) for a reason. They are implementation details the class does not want to leak to potential clients.
Generally speaking, it is a bad idea to test private and protected methods. They are not part of the public interface and they are usually executed via the public methods of a class. So when we test the public methods, they implicitly test private and protected methods.
In TDD we are testing the behavior of a class, not the specific methods. So when we make sure we test all the things a class can do, we can rest assured that the private and protected methods are tested.
If you find yourself having large private methods which need their own test, there is probably something wrong with your design. Always aim for designing small classes that do one thing.
If you still think this is nonsense and you really want to test those methods, you can take a look here on how to do that with PHPUnit.