Cessna is told about tfc, he advises in sight. 30 seconds later, XXX145 says, "Hey approach! We just got an RA about that traffic!" Me "You mean the one you reported in sight and were told to maintain a visual with?!" Him" Yeah, he was coming right at us!" Me "That's pretty much what opposite direction means".
Something very similar happened just outside of Syracuse a few years ago and before I was good at making audio clips, otherwise I would have posted it in the Audio Clips board. A Dash 8 was being vectored on a north downwind for an ILS intercept and there was a flight school Cessna 172 just north of the ILS approach at 2,000 practicing some VFR maneuvers.
The controller told the Dash 8 about the Cessna and then gave the Cessna an "at or below 2,000 feet" restriction. Moments later the Dash-8 reported traffic in sight. The controller told the Dash-8 to maintain visual and descend to 2,500.
About thirty seconds later the Dash-8 pilot announces that they are responding to an RA due to the Cessna. The controller gets on and states that the Cessna is still showing 2,000 feet but the Dash-8 pilot begins to berate him about the "close call" and starts making comments about the Cessna pilots. The controller was very professional and simply replied, "Sir, he was restricted to 2,000 and you were restricted to 2,500" and he let it go at that. I was listening to this exchange thinking, hey, what about the fact that you (the Dash-8 pilot) called "Traffic in sight?" That call doesn't give you the freedom to return to your duties inside the cockpit.
My guess was that the pilots called "traffic in sight" and then went back to both setting up the approach and running checklists, forgetting about the C172 until the TCAS alert.