If I comment the "servo.attach(portNum); " in the "My_ServoDriver_test::My_ServoDriver_test(int portNum)", and use "servoDriver.servo.attach(11);" in setup(), it works.
Of course. When your constructor is called, the pin is not ready to have a servo attached. But, it goes through the motions.
Then, the init() method gets called, and resets all the pins, to INPUT. A servo on an INPUT pin is kind of useless, don't you think?
When you perform the attach() in setup(), the pin is set as an OUTPUT pin, which lets the servo actually receive some data.
You should NOT be performing hardware-related tasks in a constructor.
Now you know why there is a separate attach() method in the servo class.
Your class should have a begin() method that does the hardware-related stuff. That method should be called in setup().