When a party member hits with an attack, a Celestial Assassin appears at the same location as the enemy that was hit, not the player who attacked.
Celestial Assassins do not count as Minions and skills that affect Minions have no effect on them. They do not count toward the Death Magic "undead servant" limit, and the "You are controlling x minions" icon is not displayed for them. They do not have inherent degeneration, do not turn hostile when their master is killed and regenerate outside of combat like normal creatures.
They appear to have no timed life span, living until they are killed by an enemy.
They do not leave an exploitable corpse.
They will not follow the party, or the player that used Star Strike to summon them. However, they will follow and attack anything the party attacks.