While they did not reveal the full plan, Lind knew as soon as they chose a direction Xing would make her move. Thus the disturbance was not tied solely to their flight path.
The ships would distribute the signal in all directions for over 5 kilometers with them as the center. Combined into an array with other ships, that effect would extend to 20 kilometers.
It had limits as they had to stay in range of the connected vessels but they could get halfway to their target before Xing could determine where they were going.
"Master, why Perot Empire?" Shi was with him as she knew the terrain of all the empires better than anyone. Also, she might have insight on the Core Hall he would desperately need if they could find it.
Despite some detailed maps in each of the conquered Empires, none had any oddities or other locations for structures that Shi had described to him. It might be underground but that would make the search very tedious.