I was looking at what an observer at Alpha Centauri would make of the ship approaching. (It is the observer that determines what is "reality") The relative motion of Earth would be irrelevant. The approaching ship would be observed at a half light year away before it would be observed one light year away. From the position of the observer at Alpha Centauri this would mean that either the ship was moving away from Alpha Centauri toward Earth or it was traveling backwards in time. Either that or we need to make some major amendments to the theory of relativity.
"Hello, Houston, no problem! We can see you!"
In the specific case of a ship using the Alcubierre drive, the ship will be observed as arriving after any photon reflected by it during its journey. However, as Bomb#20 says, the ship will be fast behind the photons, so that the ship will arrive immediately after the photons, and indeed all the photons reflected towards the observer on Alpha, by the ship during the trip, will arrive within a very short interval immediately before the ship. Anybody looking with their own eyes would just see the ship appearing suddenly out of nowhere. The film of the approach of the ship taken by an impossibly high-speed camera would show, if displayed at very low speed, the ship travelling in the right direction from the Earth to Alpha, leaving the Earth first, then moving towards Alpha and then docking on Alpha, only all this "incredibly" fast, broadly in the blink of an eye if shown in real time. No problem with causality.
Depending on how it would be done precisely, you may also have a photon trailer behind the ship. Photons coming from the Earth this time, but swept behind the ship so that, from Alpha, you'd get to see the Earth as if it was just a few months or even a few days ago, and this at least for a few seconds or hours. Again, on film, it would all look in good "order", i.e. first a four-year old Earth, then a progressively younger Earth, until you'd see very nearly the Earth as it is on the moment, and then back again with a progressively older Earth, possibly very quickly, and back to the four-year old view of it. This only on film. Looking with your eyes, you would see nothing at all except the ship itself.
No only that, but the film would make the Earth looks as if it would be itself coming closer to Alpha, in proportion so to speak of it's apparent age. So, the Earth would seem as if it was coming to Alpha, somewhat before and behind the arrival of the ship. Immediately before and after the docking of the ship, you would have a view of the Earth at the time of the departure of the ship from the Earth, i.e. at very nearly that of its arrival on Alpha. No only that, but the Earth itself, or at least a good chunk of the departure area, would look as if it had also come to Alpha, if only for a very brief moment, and only visible on film.
Time to say, "Hello, Houston, we can see you!"
We could use this to communicate in real-time. Perhaps less expensive than moving actual ships.
EB