FLT CREW OF A320 EXPERIENCE TRACK DEV IN ZMA AIRSPACE. UNABLE TO DETERMINE CAUSE.

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I WAS THE PF AND FO OF ACR X. WE TOOK OFF FROM MIAMI AND THE CLB WAS NORMAL. WE DID RECEIVE 2 CLB CLRNCS WHERE THE ENTIRE ALT CLRNC WAS OMITTED AND WE HAD TO READ A REROUTE 2 TIMES. WE ALSO REQUIRED A REROUTE TO BE READ 2 TIMES. I THOUGHT THE CTLR WAS PROBABLY AGGRAVATED WITH US. WE WERE CLRED DIRECT LAL; THEN THE CTLR SAID 'FLY A 340 DEG HDG.' WE THEN GOT DIRECT LAL. TFC WAS POINTED OUT. WE THEN GOT 15 DEGS R AND WE LOOKED FOR THE TFC BUT IT WAS IMC. SOMEHOW S OF LAL; WE MADE A TURN TO THE L WHICH CAUSED US TO CONFLICT WITH TFC. WHEN I HEARD THE CTLR SAY ACR X 2 TIMES; I STARTED A TURN R; AS INSTRUCTED; IMMEDIATELY. I WAS CONCERNED THAT I HAD NOT GONE INTO HDG SELECT AND IN FACT MADE THE 15 DEG TURN TO THE R PREVIOUSLY INSTRUCTED. THE AIRBUS IS BAD ABOUT PULLING OR PUSHING A KNOB/SWITCH AND NOT GETTING A RESPONSE; SO I ALWAYS AM CAREFUL TO CHK FMA'S. BUT I WONDERED IF THIS HAD OCCURRED THIS TIME SOMEHOW. WHEN I HEARD 'ACR X' I IMMEDIATELY TURNED R TO A HDG OF 350 DEGS AND WE PASSED SE OF LAL. ATC VERIFIED WE DID TURN 15 DEGS R; SO WE MUST HAVE BEEN IN HDG MODE AS I THOUGHT. I HAVE SPENT HRS TALKING TO THE CAPT; HRS WONDERING WHAT HAPPENED AND COULDN'T SLEEP LAST NIGHT WONDERING HOW WE MADE A TURN L AND I CAN'T EXPLAIN THIS. I SAW WINDS OF 260 DEGS AT 56 KTS; WHICH IS A DIRECT XWIND IN THE FL200'S AND THE CTLR SAID WE HAD A 100 KT L XWIND. I AM PERPLEXED. I CAN'T THINK OF REASONS FOR THE L TURN.