A FOREIGN CARRIER CAPT RPTED A MISUNDERSTANDING HE HAD WITH ZMA WHICH RESULTED IN AN ALT EXCURSION.

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WE WERE ENRTE FROM ROATAN (HONDURAS) TO MIAMI; LEVEL AT FL390; APCHING TADPO (FIR BTWN LA HAVANA AND ZMA ON G448). WE HAD TO DEVIATE TO THE L OFF COURSE (S OFF THE AIRWAY); DUE TO WX. I AS PNF ASKED HAVANA CTR; THEN HE TOLD ME TO SWITCH OVER TO ZMA ON 132.2. WHEN I FIRST CONTACTED ZMA; THE CTLR TOLD ME TO PROCEED DIRECT WEVER (WHICH IS A POINT WITH A CONSTRAINT IN THE ARR) AND THE DVALL ONE ARR TO MIAMI. I THEN REPLIED; 'ROGER ACFT X; DIRECT WEVER AND DVALL ONE ARR TO MIAMI.' A FEW SECONDS AFTER THAT; THE PF (FO) TOLD ME TO ASK FOR LOWER ALT; SO I CALLED AND SAID; 'MIAMI; ACFT X REQUESTING LOWER.' THE CTLR SAID;' ACFT X; I TOLD YOU DVALL ONE ARR.' I CHALLENGED HIM; 'I UNDERSTAND CROSS WEVER AT 10000 FT AND 250 KTS?' (WHICH IS THE CONSTRAINT). HE SAID; 'THAT'S WHAT I SAID (IN NOT TOO GENTLE WAY); SO I REPLIED AGAIN; 'ROGER; WEVER AT 10000 FT AND 250 KTS.' THE PF STARTED THE DSCNT AND WHEN WE WERE XING FL365 HE CALLED US AND SAID; 'ACFT X; WHAT ARE YOU DOING? I DID NOT TELL YOU TO DSND.' I SAID; 'YES; SIR; I CHALLENGED YOU IF WE WERE CLRED TO CROSS WEVER AT 10000 FT AND 250 KTS AND YOU SAID YES.' HE SAID; 'I DID NOT; STOP YOUR DSCNT NOW; YOU HAVE TFC AHEAD OF YOU AT FL350.' SO WE STOPPED THE DSCNT IMMEDIATELY AT FL361. AFTER THAT HE CALLED ME AGAIN AND SAID; 'ACFT X; I WILL GIVE YOU A NUMBER TO CALL WHEN YOU LAND.' I SAID; 'ROGER.' AFTER THAT HE CLRED US TO FL240; GAVE US SOME VECTORS AROUND TFC; AND TOLD US TO SWITCH OVER TO MIAMI ON 128.12. I REPLIED; 'ROGER; CONTACT MIAMI ON 128.12 AND WHICH WAS THE NUMBER YOU WANT ME TO CALL?' HE SAID; 'DISREGARD; IT'S OVER.' FROM MY VIEWPOINT; SINCE I FIRST CONTACTED HIM; I NOTICED HE WAS A LITTLE BIT STRESSED AND RUSHED. MAYBE HE WAS A NEW GUY OR HE WAS UNDER TOO MUCH PRESSURE DUE TO TFC IN HIS ZONE.