What I understand is Standby do not have its own control plane and receive relavent information from commander. This way both have FIBs in sync.
If a commander receives a packet whose egress port is on standby, the packet will traverse through VSF link nad will exit through egress port on standby switch.
If standby receives a packet with egress port also on standby switch, it will directly route that through its own egress interface (by looking at the FIB it populated through commander).
So the short answer is it Standby does route traffic based on the information is receives from Commander.