User blog comment:Dark Paladin X/Tsukasa Amane/@comment-26394425-20190830022353/@comment-405747-20190830023721

The cooldown only occurs in solo context. Notice how it only triggers if she's the only servant in the field or if the 2nd skill is used on herself instead of the other ally. I kinda designed her more of a versatile team support servant that can also serve as a solo DPS servant.

Her twin sister, Tsukuyo, will have a similar setup, but in a different take.