NMAC -- ACR HAS A NMAC WITH A CPR THAT DSNDS TOO SOON.

Narrative

APCHING JOSES ENRTE TO MIAMI FROM PAP AT ASSIGNED ALT OF 28000 FT; WITH FO FLYING; NOTICED APCHING CONTACT IN 40 NM SCALE ON TCASII 1000 FT ABOVE OUR ALT. CONTACT CHANGED TO YELLOW TA WITH DOWN ARROW BTWN 10 AND 20 NM. I TOLD THE CAPT THAT I WAS GOING TO TURN TO THE R; WHILE HE WAS ON THE RADIO TO ZMA. I STARTED A LEVEL TURN WITH AUTOPLT ABOUT 10 DEGS R. I LOOKED AT THE TCASII AGAIN AS IT TURNED RED BOX; 600 FT; WITH A DOWN ARROW AND AN AUDIBLE CLB COMMAND. I DISCONNECTED THE AUTOPLT AND PULLED THE ACFT UP. I LOOKED BACK AT THE TCASII AS THE CONTACT MOVED DOWN THE L SIDE. I STOPPED THE CLB AT FL295 AND OBSERVED THE CONTACT 1200 FT BELOW OUR ALT AND AT 8 O'CLOCK; CLR. I NEVER SAW THE CONTACT VISUALLY. WE WERE STILL IN PAP AIRSPACE JUST PRIOR TO JOSES AT ABOUT XA54. ZMA INDICATED THAT A CPR LEAR 35 MIGHT HAVE BEEN CLRED THROUGH OUR ALT BEFORE THEY SHOULD HAVE. THE CHANGE FROM MIAMI TO PAP OR VICE VERSA WITH DSCNTS STARTED AT JOSES IS A SETUP FOR THIS OCCURRENCE WITHOUT A RADAR AT PAP. ZMA INDICATED THAT WE DID NOT VIOLATE WHEN WE CLBED FOR THE TCASII ALERT. IN FACT THE TCASII PREVENTED A DISASTER. ZMA CLRED US TO LEVEL AT FL290 THEN TO FL310 AS WE INFORMED THEM OF THE EVENT AND WERE IN THEIR AIRSPACE BY THEN. THERE WAS NOT ENOUGH TIME TO TALK TO MIAMI AND PAP DURING THE EVENT AND PAP TRIED TO CLR US BACK TO FL280. THIS WAS STRAIGHTENED OUT BY EXPLAINING WE WERE NOW UNDER MIAMI CTL AND IN MIAMI AIRSPACE. SUPPLEMENTAL INFO FROM ACN 313615: ZMA INDICATED THAT POSSIBLY THE PAP CTR HAD GIVEN THE LEAR A DSCNT CLRNC AND HE HAD STARTED DOWN EARLY. THE ZMA SAID WE DID NOT HAVE A VIOLATION.