MULTIPLE RWY OP SIMULTANEOUS PARALLEL APCHS ACR X HAD LTSS FROM ACFT Y. SYS ERROR.

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DETROIT METRO ARPT WAS USING SIMULTANEOUS ILS APCHS TO RWYS 3L AND 3R; IN IFR CONDITIONS. OUR FLT; ACR X FROM PBI; WAS TOLD TO EXPECT AN ILS TO RWY 3R. WE WERE ON THE CETUS 2 ARR. FROM LISTENING TO THE RADIO TFC; IT WAS EVIDENT THAT THE CTLR WORKING OUR APCH FREQ WAS HANDLING TFC TO BOTH RWYS; AND THAT A MIXUP ON RWY ASSIGNMENT WITH A PRECEDING ACFT WAS OCCURRING. THE FINAL VECTOR TO INTERCEPT THE ILS CAUSED US TO OVERSHOOT RWY 3R AND WE BEGAN A CORRECTION BACK TO COURSE WHILE OBSERVING VISUALLY THE LIGHTS OF AN ACFT Y APPARENTLY ON THE APCH TO RWY 3L. THE TCASII GAVE AN RA TO MONITOR VERT SPD; FOLLOWED BY A RECOMMENDATION TO CLB. AS WE BEGAN COMPLIANCE TO THE RA; THE APCH CTLR GAVE US A HDG OF 090 DEGS AND CLRNC TO MAINTAIN 4000 FT; OBVIOUSLY TO AVOID THE CONFLICT. WE COMPLIED WITH THIS; AND AS WE CROSSED THE RWY 3R FINAL APCH COURSE; THE FO (PF) TURNED TO INTERCEPT. I BELIEVED THIS INCORRECT; AND ASKED THE CTLR IF WE WERE STILL CLRED FOR THE APCH (THE TCASII CONFLICT HAD CEASED). THE CTLR RECLRED US FOR THE APCH WITH A COMMAND TO SLOW TO 160 KTS; THEN SUBSEQUENTLY BROKE US OUT OF THE APCH FOR RESEQUENCING. NO FURTHER ABNORMALITIES OCCURRED. AFTER LNDG A PHONE CALL TO ATC INDICATED PRELIMINARY INVESTIGATION POINTED TO CTLR ERROR. FACTORS CONTRIBUTING TO THIS EVENT: 2 FINAL CTLRS; INSTEAD OF HANDLING TFC TO ONE RWY EACH; HAVING CONFUSION OVER SEQUENCING ACFT TO 2 RWYS SIMULTANEOUSLY.