Well, it's possible that northern hemispherers actually saw southern skies IOTL. But it would be probably dismissed as "fancy tales and nonsense" as a good bunch of the too incredible stuff that most Greeks scholars couldn't deal with, as tides or circumnavigation.
In my opinion the Greeks, especially the later ones and certainly by Roman times were probably well aware that there would be different stars in the southern sky. I'm just not sure they cared.
They knew the world was round so being able to see different stars the further south you go makes sense especially if you think the stars are stationary points. I just don't think it every really impacted their understanding of the universe.