GA SMA CLEARED ACROSS ACTIVE DOWN FIELD FROM LNDG MLG ON SHORT FINAL RESULTING IN LESS THAN STANDARD SEPARATION.

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AFTER PREFLT; RUN-UP; AND ATIS; CONTACTED CLRNC DELIVERY FOR REDHILL DEP. OBTAINED REDHILL DEP. ADVISED HNL GND CTL MODEL A SMA X; ON NORTH RAMP TAXI FOR DEP. GND CTL CLRED SMA X TO TAXI TO 8L AT INDIA. ON ALPHA TXWY JUST PRIOR TO 8L INDIA; GND TOLD ME TO MONITOR TWR ON 118.1. TURNING ONTO INDIA; I MONITORED TWR 118.1. I RECALL TWR ASKING IF MODEL B SMA X WAS UP. I SAID SMA X WAS WITH HIM; THEN TWR SAID; 'SMA X CROSS RWY (BELIEVE 8L) WITHOUT DELAY; CLRED FOR TKOF 4L.' I LOOKED TO RIGHT AND SAW AN ACFT ON SHORT FINAL. I BELIEVE IT WAS AN ACR-MLG. I THEREFORE UNDERSTOOD THE REASON FOR NO DELAY. I KNEW I COULD CROSS BEFORE T/D OF THE MLG AND EXPEDITED ACROSS 8L. AFTER XING 8L I LOOKED BACK TO RIGHT AND NOTED THAT MLG WAS JUST LNDG. I SEEM TO RECALL HE TURNED LEFT AND CLRED RWY AT GULF TXWY APPROX 3000' UP FIELD OF 8L AT INDIA. I THEN HELD SHORT OF 4L AND WANTED TO RECONFIRM I WAS CLRED FOR TKOF ON 4L. TWR CTLR HANDLED SOME OTHER TFC THEN I CALLED AGAIN TO CONFIRM MODEL A SMA X IS CLRED FOR TKOF 4L. TWR CTLR ADVISED; SAID SMA X CLRED FOR TKOF 8L. I ADVISED THAT I CROSSED 8L AS INSTRUCTED AND WAS HOLDING SHORT OF 4L UNTIL CONFIRMED CLRED FOR TKOF 4L. TWR SAID CLRED FOR TKOF 4L. THE REASON I HELD SHORT OF 4L WAS BECAUSE I NOTED THE MLG ON SHORT FINAL PREVIOUSLY; BUT WANTED TO MAKE SURE THAT THE MLG WAS GOING TO CLR UPFIELD AND THAT NO PROB WAS GOING TO COME UP IF I DEPARTED 4L AS I WAS CLRED FOR TKOF. I DEPARTED 4L; TWR SWITCHED ME TO DEP AND WAS NOT AWARE OF ANY PROB. CLRED THE TCA AND PROCEEDED ONTO DILLINGHAM FIELD. AFTER APPROX 1 HOUR; I RETURNED TO HNL. I OBTAINED ATIS; AND CONTACTED HNL APCH CTL ON 119.1 PRIOR TO TCA ENTRY. AFTER RECEIVING SQUAWK AND CLRED INTO TCA; APCH ASKED ME TO GIVE THE TWR A CALL AFTER ARRIVING HNL. UPON ARR HNL; I CONTACTED TWR AS ASKED. I SPOKE WITH THE SUPERVISOR WHO ASKED ME FOR FULL CALL SIGN OF THE ACFT. I ADVISED AND HE ASKED MY NAME. I TOLD HIM. I ASKED WHAT THIS IS IN REFERENCE TO. HE SIMPLY SAID THAT EARLIER AN ACR-MLG WAS ON SHORT FINAL TO RWY 8L AND I WAS OBSERVED XING 8L; AND THERE WAS AN INVESTIGATION INTO THIS XING OF 8L. HE WAS NOT CLR AS TO WHETHER OR NOT HE FELT I WAS THE PROB OR CTLING WAS THE PROB. HE ALSO SAID HE NEEDED THE INFO TO SUBMIT HIS PAPERWORK. I EXPLAINED AS I HAVE PREVIOUSLY OUTLINED IN THIS DESCRIPTION; HE TOLD ME THAT HE BELIEVED THE CTLR TOLD ME TO CROSS 4R; CLRED FOR TKOF 4L. I THOUGHT TO MYSELF; THAT COULD NOT BE POSSIBLE SINCE I WAS ON THE OTHER SIDE OF THE RWYS. ANYWAY HE SAID I WOULD BE CONTACTED IF NEED BE. I WISH TO NOTE TWR LOCATION MAKES CTLR VIEW APPROX 180 DEG FOR ARRIVING TFC TO 8L AND DEPARTING TFC DOWNFIELD. THEREFORE SUGGEST MORE SEP BTWN ARRIVING TFC ON 8L AND DEPARTING TFC DOWNFIELD. CALLBACK CONVERSATION WITH RPTR REVEALED FOLLOWING INFO. CONVERSATION REVEALED THAT THE TWR TAPES REVEALED THAT SMA X DID REPLY TO THE CLRNC WITH 'SMA X EXPEDITE ACROSS 8L CLRED FOR TKOF 4L.' IT ALSO REVEALED THAT SMA Z A DIFFERENT MODEL ACFT WAS COMING OUT FROM THE SE RAMP AND THE LCL CTLR MIXED THE CALLSIGNS AND HAD SAID FOR MODEL B SMA X TO EXPEDITE ACROSS 4R CLRED FOR TKOF ON 4L. SINCE SMA X WAS NOT A MODEL B PLT ASSUMED CTLR HAD JUST USED THE WRONG MODEL SINCE HE HAD USED THE CORRECT CALLSIGN AND SINCE NO CHALLENGE OF READBACK AND HIS PERCEPTION MLG WAS NOT YET OVER DISTANT THRESHOLD TAXIED AS CLRED. ALSO STATED IMPRESSION HE GOT FROM TWR PERSONNEL WAS THAT THEY THOUGHT WAS OPERROR. HE HAS HEARD NOTHING MORE FROM THEM. ALSO SINCE THE MODEL B SMA Z WAS NOT ON FREQ HE HAD NOT MOVED.