How did Skyler Base miss Winfall's disappearance? Part 2

Yesterday, we saw that Rei was able to figure out how the Vuduri missed the Winfall disappearance. He told OMCOM that traveling faster than light had to have some effect on the flow of time. OMCOM felt it his duty to bring Rei’s theories to the attention of Commander Ursay. If anything, the Commander was even more skeptical than OMCOM:

     It was clear that speaking to Rei was a physical affront to the man. Rei ignored it. “Well, when you are approaching the speed of light, time slows down. But when you exceed the speed of light, maybe it speeds up, goes backwards, who knows? Maybe you guys just think you are farther along into future than you thought. Maybe the star disappeared right on time and maybe it was just your clocks that were off.”
      “Impossible, our clocks are always correct when we return home.”
      “Maybe it is relative to the clocks you travel away from? And toward. Maybe you carry your frame of reference with you. I really don’t know and I don’t know why OMCOM bothered you with this. It’s just that…”
      “Just that what?” Ursay asked.
      “It’s just that traveling faster than light has to have some implication with regard to the regular speed of light and time and what not,” Rei said. “It just doesn’t seem like you could get away unscathed by relativity.”
      “It has not affected us at all, not even once,” Ursay said firmly. “Everything always works out correct. Is this all you have?”

Rei’s arguments were cogent enough that even OMCOM had to admit their possibility. The computer was intrigued enough that he and Rei rigged an experiment. They sent a space tug out past the light waves of Winfall's disappearance and at the same time, OMCOM beamed a time-encoded laser off of the tug. The reflection could be compared to the transmissions from the tug. When the signals came in, OMCOM tried to save face by minimizing the fact that a human was able to outthink the great and powerful OMCOM:

     The evidence was irrefutable although OMCOM refused to make a big deal of it. At least he did admit that Rei was correct: “Did you ever get the calibration signal back? The one you bounced off of it?” Rei asked OMCOM.
      “Yes.”
      “And…”
      At first, OMCOM did not reply. Finally, he said, “You were correct. There is a small discrepancy.”
      “I told you!” Rei said. “You can’t just go flitting about faster than light without some reckoning.”
      “I will consider the mathematics and develop a theory,” OMCOM said. “Now that I am aware of it, I will compensate. It will have no bearing on the immediate operation, regardless. I am going to send the probes to the wavefront now.”

Even though he would not tell Rei, OMCOM did make a note to pay attention to Rei’s ideas in the future.