It's a seemingly simple association to make.
Even if they didn't know the name Tilani at that time, the Red Moon and Annalise were right there in plain sight.
The reason Fu Qian didn't immediately probe in that direction was because several core conflicts were also evident.
For example, a most pressing one: If it really is the Red Moon, why didn't it recognize me?
Considering the separate behaviors of the Red Moon and Prism of Radiant Transformation in Night Holy City, it's clear that the former indeed lacked agility, unable to track me into the mission.
But during the mission on the Archipelago, it was like I directly intruded on its home ground.
Even using my true appearance, with only a barely concealing mask, having done no disguise at all.
Yet, the Red Moon seemed utterly unresponsive.
Now, however, "Annalise and Tilani" seem to subtly explain this point.
