My hypothesis for pointing at the star when in system is.Fascinating thread. So glad I stumbled on it. Why would they aim at the star (when in system)? If they are "friendly" perhaps that's the first system they'll jump to before approaching the bubble? Aka, "we see you, now look where we're pointing"? Also, if they're transmitting a morse code type language reflecting the ships they scan, isn't that an acknowledgement that they "recognise" us as a star fairing species? IOW, could they be suggesting a diplomatic meeting place for first contact?
It is designed to report back to somewhere in Merope from other systems, so is programed to point at the star, that's as accurate as us required. It is not designed to be used in Merope, but continues to follow it's programming. Just as RL earth probes are programmed to point at earth, not specifically at the receiving station.