It's not a homing attack, the symbol just spawns right in any part of your body.
First move is irrelevant since the match's rule said both characters have prior knowledge on each other, this is a stand off one hit kill situation, both Sans and Cyn can actually kill each other.
But if you want to know what's her first move, in Episode 8, Cyn first teleported behind Uzi and went straight for her core with her bare hand. The reason for that is because Uzi and Cyn are both Solver Users, solver users are immune to each other's Solver so Cyn couldn't spawn a Null in her body and they have to rely on their strength. But to non-Solver users, it would be a different case just like Doll did to other non-solvers.