If we look south in any location in the southern hemisphere, we will see the same set of stars. The stars are seen rotating around the south celestial pole, in the Octans constellation, near the star Sigma Octantis.
This phenomenon can never be explained in the flat-Earth model. Looking at the so-called ‘flat-Earth map’, we should see another set of stars on a different location in the southern hemisphere. The reason is that the flat-Earth model is a false representation of the Earth.
As an example, we will use five cities: Sydney (Australia), Papeete (Tahiti, French Polynesia), Santiago (Chile), Johannesburg (South Africa), and Jakarta (Indonesia).
If the Earth is flat, then observers on the different cities will face opposite each other, and therefore everyone should see different stars. In reality, all of them will see the same stars, only with different orientations. This observation is only consistent with the spherical Earth model, and cannot be explained with the flat Earth model.
The flat Earth model was initially designed for the northern markets without much regard for what is happening in the southern hemisphere. Back then, it is not that easy for northerners to observe the southern stars, and it was very difficult for most of them to confirm that the flat Earth model is nonsense. All of us live in modern times and do not have such an excuse, especially those of us already living in the southern hemisphere.