If you're flying in low latitudes, nearly half the stars that you want to use are going to have negative declination, so negative declinations are important. As for the hemisphere switching, this happened automatically.
It's totally normal to be in the northern hemisphere and looking at stars below the celestial equator. For instance, Sirius is the brightest star in the night sky and is in the southern half of the celestial sphere. So if you wanted to navigate with Sirius, the system had to support negative declination. (They define negative declination as in the opposite N/S hemisphere from the aircraft.)
