HDG TRACK DEV DURING TSTM AVOIDANCE PROC BY THE FLT CREW OF AN A319 40 MI NW OF NUCAR INTXN ON FREQ WITH ZMA.

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THIS INVOLVES A PROB WITH A CTLR WHILE DEVIATING AROUND WX SBOUND ON AR-3. THERE WAS TSTMS ALONG THE AIRWAY AND WE WERE CLRED TO DEVIATE AS NECESSARY WITH A 20 DEG LIMITATION R OR L. WE JUST MADE A R DEV AND WERE PARALLELING THE AIRWAY. WE THEN BEGAN A L DEV WITH A TSTM AHEAD. IT BECAME APPARENT THAT WE NEEDED TO DEVIATE MORE THAN 20 DEGS. WE DISCUSSED WHERE WE WANTED TO GO. SINCE WE WERE IN CLOSE PROX TO A CELL; I TURNED MORE THAN 20 DEGS TEMPORARILY AND ALMOST SIMULTANEOUSLY THAT CAPT ADVISED ATC OF OUR NEED FOR A GREATER TURN. ATC IMMEDIATELY YELLED (LITERALLY) AT US ACCUSING US OF VIOLATING THE 20 DEG DEV RESTR. HE APPARENTLY HAD AN ACFT BEHIND US AND WAS CONCERNED ABOUT SEPARATION. THERE WAS NO TA/RA. THIS COULD HAVE BEEN PREVENTED IF ATC HAD ADVISED US THE REASON FOR THE RESTR AND THUS WE WOULD HAVE BEEN AWARE OF THE TIGHT SEPARATION. WE PROBABLY COULD HAVE SPOKEN SOONER; BUT DUE TO THE DYNAMIC NATURE OF THE WX WE WERE NOT SURE OF THE HDG WE WERE GOING TO USE. DUE TO CHATTER WE COULD NOT GET A WORD IN EARLIER.