MULTIPLE RWY OP PARALLEL RWYS ACR X HAD LTSS FROM ACR Y. SYS ERROR.

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MIA ATC TWR; E OP RWYS 9L; 9R AND 12 ACTIVE. 2 LCL CTLS; N AND S. I WAS WORKING CAB COORD N (CCN). I RECEIVED POS RELIEF BRIEFING FROM LCN TO OPEN CCN POS WHILE IT WAS BUSY; MODERATE TO HVY TFC. THE BRIEFING WAS QUICK. DURING THE BRIEF I WAS LED TO BELIEVE THAT LCS HAD RECEIVED RELEASES FOR 2 DEPS FROM LCN. THE DEPS BEING A NBOUND TWIN PROP AND A SBOUND HVY JET. ON AN E OP LCS OWN RWY 9R FOR ARRS; BUT DOES NOT OWN ANY DEP HDGS AND MUST COORD FOR RELEASES WITH LCN OR CCN. I WAS UNDER THE IMPRESSION THAT THE RELEASES HAD BEEN COORD; WHEN IN FACT THEY HADN'T. AFTER BEING ON POS 40 SECONDS; I CALLED LCS TO CONFIRM THAT LCS WAS RELEASED ON THE TFC DEPARTING RWY 12. AT THAT TIME LCS SAID THEIR RELEASES WERE ON A NBOUND PROP AND A NBOUND HVY JET. I ALSO WANTED XING CLRNC FOR 2 ACFT DOWNFIELD RWY 12. AT THAT POINT I STARTED SCANNING RWY 12 TO MAKE SURE IT WAS CLR AND I DIDN'T HEAR NBOUND HVY. LCS ROLLED ACR X; HDG 090 MAINTAIN 50 OFF RWY 9R. LCN THEN ROLLED ACFT Y HDG 090 MAINTAIN 50 OFF RWY 9L. THE 2 ACFT AUTO ACQUIRED SIDE BY SIDE 1 MI APART. LCN; LCS OR MYSELF DID NOT CATCH THE MISTAKE UNTIL DEP CTL HAD ESTABLISHED VISUAL SEPARATION. AN OPERROR WAS FILED ON ME AS CCN; AS WE HAD NO FORM OF SEPARATION OFF THE ARPT.