Yes, and what they also dont appreciate is that whenever it is seen, it will be at the same relative position at the same time.
So for example, when the southern cross is seen from New Zealand, lets say at 01:00 local time there, and then seen from Perth, say at 20:00, it will look exactly the same with the long axis of the cross inclined at the same angle relative to the South Pole axis. For example, looking like it was pointing at 11 o’clock. Taken at the same moment (UTC) it would look identical to both observers.
I cannot say i agree with Edby that there is agreement among FEers that there is a southern axis of rotation.
EnaG specifically says there cannot be, and Sigma Octantis tracks along the circumfrance, the wiki describes all the stars rotating about Polaris, so it would be impossible for Sigma Octantis to be an axis as well.