It is worth noting that, if we take those words at face value, they are the wrong words. What actually appears to your eyes, or to your telescopes or other instruments, is not a drastic change in "distance" in a short time. All that actually appears to your eyes and instruments is a drastic change in the redshift of light coming from Alpha Centauri--from "strongly redshifted" (because you were moving away from AC at close to the speed of light) to "no shift" (in the idealized case where Earth and AC are at rest relative to each other).
Actually, in the presented case of rapid deceleration from very fast to 0 (relative to Earth) cause the image of AC to shrink so as to make it appear further away (in addition to blue shifting)? In a spacetime diagram, I notice the distance the light has traveled as the ship arrives at Earth in the frame where it is still moving is much less than the distance it appeared to have traveled in the frame where it has stopped at Earth. That suggests to me the image of AC would "zoom away" to make it look as if it receded from you at that moment. It points to the fact that things you are moving away from appear to be closer to you and receding from you at a slower speed than they actually are (when considering the appearance from observing the light), while things you're moving toward appear further away and appear to approach you faster than they are (potentially faster than c).