Yes, they need to be connected per the instructions. It will not only make the difference in the motor working, it will also determine if the motor turns clockwise, or counter-clockwise. Very important if you want the cyclone to move air properly to work as it is designed. The wires in the motor connection box are labeled to match the diagram. The two hot wires from the breaker box can be interchanged without any issues.
Also, make sure all of the wires in the diagram are present. My motor, ordered directly from Electric Motor Warehouse came with the bare end of one of the wires mounted between the motor box and the motor housing. I all but threw the switch when a little voice said to go back and check the wiring again. No telling what would have happened if I hadn't found the problem. Hope this helps! Jim.