Does the DCW need to be turned 180 degrees when 1237 or 1238 is installed upside down? Does it make any difference?

Main motivation for rotation of DCW (Directivity Control Waveguide) is to enable changing speaker orientation between horizontal and vertical. Tweeter and midrange should be on top of each other. If they are side by side, there will be acoustic cancellation at crossover at horizontal listening plane. 

Other side effect of rotating the DCW is change in location of acoustical axis. In example, looking at 1237A views, you see that flipping the DCW moves the acoustical axis towards woofer. It depends on your installation, where you want to have the acoustical axis.