LCL CTLR DESCRIBED CONFLICT BTWN 2 ACFT ON VISUAL APCHS TO PARALLEL RWYS; NO OPERROR RECORDED.

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AT APPROX XA00 I WAS INFORMED BY SUPVR THAT I WOULD BE ASSIGNED THE LCL CTL PSN. HE PRE-BRIEFED ME THAT N90 WOULD ATTEMPT TO RUN OVERFLOW TO RWY 4L WHILE THE PRIMARY ARR RWY WOULD BE RWY 4R. I ASKED IF N90 WOULD ESTABLISH VISUAL SEPARATION WITH THESE ARRS PRIOR TO XFER OF CTL AND THE SUPVR RESPONDED IN THE AFFIRMATIVE. AT APPROX XA10 THE FIRST RWY 4L ARR AND THE FOLLOWING RWY 4R ARR WENT INTO CONFLICT ALERT MODE. I WAS NOT IN CONTACT WITH EITHER OF THESE ACFT AND COMMENTED TO NOBODY IN PARTICULAR 'WATCH THEM SWITCH THESE GUYS AND NOT HAVE THE OTHER IN SIGHT.' WITHIN SECONDS THE RWY 4R ARR WAS ON MY FREQ WITH APPROX 1 MI OF SEPARATION WITH THE RWY 4L ARR (WHO I WAS NOT IN CONTACT WITH). I ASKED IF HE HAD THE RWY 4L ARR IN SIGHT; TO WHICH HE STATED NO. I TURNED TO THE SUPVR AND EXPLAINED THE SITUATION UNFOLDING AND HIS RESPONSE WAS SOMETHING TO THE EFFECT 'IT'S THE FIRST ONE; GIVE 'EM A CHANCE TO GET IT RIGHT.' I REITERATED THE FACT THAT I THOUGHT THIS WAS A DEAL AND RECEIVED AN INCOMPREHENSIBLE RESPONSE.