How to determine sign of voltage with a current source in series
Why is there a change of sign in voltage (i.e. +12V for B and -12V for
A)?

Not quite. What you should get when you rotated the circuit was this: -

And now, both nodes will have the same polarity voltage.
So, if you actually did reposition the GND node to where you show it in your original picture, the voltage polarity would reverse. But that ain't a simple rotation!