Jim,
The Black and Red are universally the two hot legs and the white is the neutral. You can verify that with a meter, you should see 120V from white to black and 120V white to red at the relays of the transfer switch. Those are your two hot legs coming to the transfer switch.
Regardless of how the protection device labels things as leg one or two is not an issue. You would follow their color code and maintain red to red, black to black, and white to white through the protection device and through the transfer switch. That is, wire the transfer device as it is now and the protection device as they show it in their literature and follow the color code black to black, red to red, white to white through both.
Later Ed