B727 RECEIVES CLRNC AS FILED AND FOLLOWS SID. TWR DELAYS HDOF TO CTR FREQ. CTR CTLR CHANGES HDG IN AN EVASIVE MANEUVER TO AVOID OTHER CONFLICTING TFC. RPTR CITES AN ATC COORD PROB IN TWR FAILING TO GIVE AMENDED HDG INFO.

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WE FILED THE KODIX 2 DEP OUT OF SDQ TO MIA WHICH CALLS FOR A L TURN AFTER DEP TO INTERCEPT W4 (351 DEG RADIAL OFF OF CDO). CLRNC WE RECEIVED WAS 'AS FILED; CLB TO FL310; CLRED FOR TKOF.' NO DEP FREQ GIVEN AND NO FURTHER INSTRUCTIONS. AFTER TKOF WE NOTICED 2 ACFT TO OUR L AT APPROX SAME ALT AND 5 MI AWAY ON TCASII. WE VISUALLY LOOKED AND NEVER DID SEE THE OTHER ACFT. WE MONITORED OUR TURN IN RELATION TO THE TCASII DISPLAY AND WERE ABOUT TO ASK THE TWR FOR A FREQ CHANGE WHEN TWR EXCITEDLY CALLED AND SWITCHED US TO SDQ CTR ON 119.3. CHANGED FREQ AND SDQ CTR CTLR VERY EXCITEDLY ASKED WHY WE HAD TURNED L AFTER TKOF WITHOUT CLRNC. WE EXPLAINED OUR CLRNC AND HE WENT QUIET. I BELIEVE CONTRIBUTING FACTOR IN CONFUSION IS THE LANGUAGE DIFFERENCE BTWN US AND THEM. SDQ TWR NEVER GAVE US THE CLRNC THAT SDQ CTR WANTED US TO RECEIVE. NEVER GOT CLOSER THAN 5 MI TO OTHER ACFT. SUPPLEMENTAL INFO FROM ACN 365010: WE FLEW THE DEP AS PUBLISHED. AFTER SWITCHING TO SDQ CTR; THEY NOTIFIED US THAT WE WERE SUPPOSED TO MAINTAIN RWY HDG AFTER DEP. AT THAT TIME WE WERE LEVEL AT 4000 FT MSL. WE WERE INSTRUCTED TO IMMEDIATELY TURN R APPROX 30 DEGS TO HDG 020 DEGS. THERE WAS ALSO SOME DISCUSSION ABOUT OPPOSITE TFC AT THE SAME ALT.