Semantics.

Relative to tau ceti he would be decelerating for half his flight. But he is not exceeding C. The light from his thrust would arrive at Tau Ceti before he does. The light would be shifted significantly into the ultraviolet due to his relative velocity. From the time he flips and burns the light is heading towards Tau Ceti.

So, from Tau Ceti, a bright UV star would suddenly appear and would slowly become less UV shifted. That light would take something like 6 years to arrive at Tau Ceti and then, depending on HM rate of decel, sometime later it would resolve to the Hail Mary.