At the last minute, Kyran decided to intervene in the battle between the Armakea and Eidum using his Draconic magic. He came to this decision after much deliberation.
The Shaiha masked his aura and magic, and warping to Cyneah's location would not reveal himself to those outsiders observing from afar per se. But that was not his immediate concern. Instead, he was worried about how the mirror would react once he appeared.
It should be noted that his first encounter with the Macabre Glacier, it managed to influence the Shaiha easily. If that happened, the latter would go haywire. After that, it would stop concealing his aura and magic, which would then reveal his presence.