Well, I can't speak for the entire team, but I believe that Diaspora is the root of the English phrase 'Disperse' or possibly 'Displace', which means more or less the same thing, to spread out from a fixed point, in this case, the colonies.
As the Pegasus proved, the Galactica's belief that they alone survived the Cylon attack on the colonies is not neccesarily a fact written in stone. In Greek history (which does, I'll agree, have a pretty hefty influence on BSG), the Diaspora referred mostly to the movement of Greek culture throughout the Mediterranean area and beyond, in this case the Diaspora would refer more to a refugee status than a cultural spread as bought about by the growth of Greek culture, which culminated in Alexander the Great, the Diaspora mentioned here would probably be more akin the displacement of peoples through war and hardship, seeking a new and better life.
