A319 FLT CREW HAS A RWY INCURSION DURING TAXI FOR TKOF AT MBPV.

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WE WERE CLRED TO TAKE THE ACTIVE RWY AND BACK TAXI AND HOLD FOR TKOF CLRNC ON RWY 28 AT PROVIDENCIALES ISLAND (MBPV). MY FO READ BACK THE CLRNC TO THE CTLR ON 126.0. ALL OPERATORS AT THE ARPT WERE BEING PERFORMED ON 126.0 (PROVO APCH). 1/2 WAY THROUGH THE BACK-TAXI I NOTICED A BEECH 1900 OR SKY KING THAT LOOKED LIKE HE WAS ON L BASE FOR RWY 28. I MENTIONED THIS TO MY FO. ABOUT THAT TIME PROVO APCH ASKED OUR POS. WE TOLD HIM WE WERE BACK-TAXIING FOR TKOF POS. (I REALIZE NOW THAT APCH CTL IS NOT LOCATED IN THE TWR AT THE ARPT. I ALSO REALIZE THAT BECAUSE HE ASKED WITHOUT ANY PROMPT FROM US OR SKY KING THAT HE KNEW THAT HE HAD FORGOTTEN THAT THEY WERE ON A VISUAL APCH WHEN WE CLRED US FOR BACK-TAXI). REMOTELY LOCATED APCH RADIO SHOULD NOT RUN ALL ARPT OPS. WE WERE TOLD TO RETURN TO THE RAMP AND SKY KING WAS TOLD TO PERFORM A 360 DEG TURN BEFORE CONTINUING APCH. SUPPLEMENTAL INFO FROM ACN 694294: HE IMMEDIATELY ASKED A 'SKY KING XXX' WHAT HIS POS WAS. HE REPLIED '3 MI FINAL RWY 28.' HE WAS TOLD TO MAKE A R 360 DEG TURN AND REJOIN FINAL. WE WERE INSTRUCTED TO MAKE A 180 DEG TURN AND EXIT RWY 28 AT BRAVO. WE SAW THE TFC AND COMPLIED.