Solomae,
More than likely you'll need to loosen the belt. A too tight belt will drag the motor down causing it to run slower and take more amps to turn. It only needs to be tight enough that it doesn't slip, no tighter.
The old controller is functioning properly. It is a resistance type controller and it's normal for them to get warm. It's probably allowing more amps to the motor at the start than the electronic one. Hense the motor starts turning when you push on the button.
Joe