A319 FO REPORTS UPSET ZTL CONTROLLER AND TCAS TA WHILE DEVIATING AROUND TRW'S AS CLEARED AT FL280.

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ON CLBOUT; WE LEVELED OFF AT FL280 INSTEAD OF INITIAL CRUISE FL320 DUE TO RPTS OF MODERATE TURB AT FL320. WE WERE ONLY EXPERIENCING LIGHT TURB AT FL280 IN VMC. WE WERE CLRED BY ZTL TO DEV L AND R OF COURSE DUE TO TSTMS IN THE AREA. AS THE CAPT WAS DEVIATING; WE WERE SWITCHED TO ANOTHER ZTL FREQ WHO IMMEDIATELY ASKED US (I THINK) FOR OUR HDG AND ALT. I REPLIED. THE CTLR IMMEDIATELY TOLD US TO DSND TO FL270; WHICH WE STARTED TO DSND. I REPLIED AND TOLD HER THAT WE WERE CLRED TO DEVIATE AROUND THE WX BY THE PREVIOUS CTLR. WHEN I RELEASED MY MIKE SWITCH; I REALIZED SHE HAD ALREADY BLOCKED MY XMISSION AND THE LAST WORDS SHE WAS SAYING WERE 'CALL SIGN; DSND TO FL270 NOW!' AT THE SAME TIME; I LOOKED DOWN AT MY NAV DISPLAY AND SAW A TARGET 2 O'CLOCK POS AT FL280 AND WE GOT THE 'TFC; TFC' TA. THE UPSET CTLR ASKED US IF WE WERE DSNDING; AND I REPLIED THAT WE WERE PASSING FL276. SHE THEN SAID 'CALL SIGN; RPT FL270 IN 30 SECONDS.' WE RPTED LEVEL AND SWITCHED US TO ANOTHER FREQ. I DON'T KNOW HOW THIS HAPPENED SINCE WE WERE SUPPOSEDLY UNDER RADAR CTL AND WHY WE WERE SUDDENLY IN A TFC CONFLICT WHEN WE WERE CLRED TO DEV AROUND THE WX. I'VE LEARNED TO NOW KEEP A WATCH ON TFC UNDER RADAR CTL EVEN WHEN 'CLRED TO DEV.'