UNKNOWN CORPORATE ACFT WAS HIGH DUE TO LATE DSCNT CLRNC WHEN APCH CTLR TURNED FLC OVER TO TWR CTLR. TWR CTLR TOLD THEM CLRED FOR STRAIGHT-IN VISUAL AND TO RPT THE RIVER. BECAUSE THEY WERE HIGH RPTR CAPT DID A 360 DEG TURN FOR LOSS OF ALT; TWR QUESTIONED THEIR ACTION BECAUSE THERE WAS AN ACFT FOLLOWING THEM. TFC WAS UNKNOWN TO FLC.

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ENRTE FROM CLE TO PKB; WE WERE CLRED FOR DSCNT INTO PKB. OP WAS IFR; THROUGH ZID; AND IN CAVU CONDITIONS. DUE TO A DELAY IN THE DSCNT CLRNC; WE ARRIVED IN THE PKB AREA TOO HIGH FOR THE EXPECTED STRAIGHT-IN VISUAL APCH TO RWY 21. ZID TERMINATED RADAR SVC AT 6000 FT AND INSTRUCTED US TO CONTACT PKB TWR; WHICH ISSUED A VISUAL APCH TO RWY 21 AND TO RPT 'XING THE RIVER.' DUE TO THE ALT AND PROX; I ELECTED TO MAKE A DSNDING 360 DEG TURN FOR POS. AFTER RPTING THE RIVER INBOUND; TWR ASKED IF WE HAD MADE A 360 DEG TO WHICH I REPLIED AFFIRMATIVE. AFTER ARR I WAS REQUESTED TO CALL THE TWR. WHILE TALKING WITH THE CTLR; A CONFERENCE CALL TO IND WAS ESTABLISHED. IND INFORMED ME THAT THEY HAD HAD TFC FOLLOWING ME FOR PKB AND THAT THERE COULD HAVE BEEN A POSSIBLE CONFLICT. ALTHOUGH WE HEARD IND TALKING TO OTHER ACFT; WE WERE NEVER ADVISED OF ANY POTENTIAL PROB OR EVEN OF ANY OTHER AREA TFC. IN RETROSPECT; ALTHOUGH I ASKED THE FO TO INFORM THE TWR OF THE INTENDED 360 DEGS; I DON'T RECALL THAT XMISSION. HAD ZID APPRISED US OF THE FOLLOWING TFC; WE COULD HAVE AVOIDED THE PROB. THIS WAS A CLASSIC CASE OF LACK OF COMS ON BOTH PARTS. THERE WAS NO CLOSE CALL; BUT THE POSSIBILITY EXISTED.