It can contain an identifier, but does it have to?
Of course it will. From a software engineering perspective, a network protocol that can't distinguish between different senders and receivers is of rather limited use.
And even if it didn't it doesn't need to for them to correlate it with the aircraft.
Presumably the satcom system "transport layer" was pinging satellites from takeoff (even if other systems on the aircraft were not trying to send data), and thus plotting the progression of pings will indicate the flight path from takeoff.