If it's NOW in the Sol system, it's NOW in Alpha Centauri as well. (I guess it's difficult to think in these terms because we always only see a 4.367 years old "NOW" from Alpha Centauri.)
There would be no violation of Causality if you had a ship which could instantly Jump between Sol and Alpha Centauri - you'd simply arrive there at NOW+<however long this Jump took> - whether it's seconds or picoseconds.
If you sent a radio signal "Hi there!" from Sol to Alpha Centauri before this Jump, you'd be waiting for 4.367 years for it to arrive - which still isn't a violation of Causality, because it'd be NOW+4.367 years in Alpha Centauri and the same would be true in the Sol system.
If your faster-than-light (faster-than-Causality) Drive wasn't an instantaneous Jump like above, Causality is still not violated, because you'd still be arriving at NOW + <however long it took> to travel between Sol & Alpha Centauri. Maybe you could only travel at twice the speed of light (twice the speed of Causality), in which case you'd arrive there in NOW + 2.1835 years
The problem with this is that there is now an unaccelerated, moving (with relation to here/Alpha Centauri) system in which you appear in AC before you leave here, i.e. break causality.
But that system would see a strange thing but it wouldn’t be sending information backwards because they wouldn’t be able to act on that information on earth or AC.
Maybe it’s the same as how I can move a beam of light across the moon faster than light but that’s ok since it can’t send information.
That's called having a privileged reference frame, and yes, if your FTL jumps all use the same reference frame then there's no way to violate causality.
