In the United States, ATC professionals do not need to notify both aircraft of a point out. It is procedure to only notify one. In this case the tower controller was probably compliant.

PAT told the controller twice he had the aircraft in sight. PAT requested twice to maintain visual separation. PAT accepted legal responsibility twice. PAT did exactly what he said he would not do, impact the conflicted airliner.

There are a lot more safety concerns here I hope are addressed soon. The behavior of PAT seems blatantly incompetent. It's hard to accept such a screw up.