Just to add to FlytheTail and ORDnHKG: If the OP does a dummy booking SGN-ICN for the specific date in November he will be shown seat selections for "777-300"(with seat selection showing new F and J configuration) or "777-200" (with seat selection showing old F and J configuration) for the late evening flight 736...I assume this is the one they are on...
So #736 SGN-ICN can be either the ICN-JFK/LAX(or wherever the new J & F fly) originator or the ICN-ORD plane. Sounds like the ORD 236/235 plane from the agent's description meaning old J and F with J service. Again, a dummy booking will show the currently assigned aircraft.