C750 FLC REACTS TO MULTIPLE TCASII ALERTS DURING TEST FLT MANEUVERING. PIC ASKED TO CALL TRACON ON LNDG TO DISCUSS SIT.

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MANEUVERING VFR IN VMC; RESPONDED TO TCASII RA; VISUALLY ACQUIRED TARGET -- NO FACTOR. DURING APCH INTO ICT; ATC ASKED US TO CALL ATC ON LANDLINE. THEY SIMPLY WANTED US TO CONSIDER STAYING IN RADIO CONTACT WHILE MANEUVERING. SUPPLEMENTAL INFO FROM ACN 426244: ROUTINE TEST FLT PERFORMED. DEPARTED ICT TO W AND ONCE OUT OF CLASS C; RADAR SVC CANCELED. CONTINUED VFR ABOVE CLASS C AT 10500 FT; IN WHICH MANEUVERING FLT FROM W TO E AND E TO W TRACKS WITH INTERIM TURNS TO N AND S. OUR TCASII WAS ON AND FUNCTIONING AND WE HAD RECEIVED TA ALERTS FOR A COUPLE DIFFERENT ACFT. VISUAL CONTACT WAS MADE ASSOCIATED WITH ALL TA TARGETS; WITH CLOSEST ENCOUNTER ESTIMATED AT 600 FT VERT AND 1 1/2 MI HORIZ. AT NO TIME WAS AN RA RECEIVED. TESTING CONTINUED FOR ANOTHER 15 MINS; AT WHICH TIME RADAR SVC RE-ESTABLISHED. THE INITIAL CTLR THEN INFORMED US THAT TRACON REQUESTS WE GIVE THEM A PHONE CALL AFTER LNDG. CALLED TRACON LATER THAT EVENING AND THE ATTENDING CTLR INFORMED ME THAT HIS SUPVR WAS CONCERNED THAT APPARENTLY THE 600 FT AND 1 1/2 MI ENCOUNTER ACFT HAD RPTED THEY INITIATED EVASIVE ACTION TO AVOID OUR ACFT. IT WAS UNKNOWN WHETHER THE OTHER ACFT WAS USING TCASII; BUT THE CTLR INFORMED ME IT WAS A FALCON. THE CTLR SAID AFTER THE FALCON RPTED EVASIVE ACTION; APCH BEGAN TRACKING US. BASICALLY THE CTLR SUGGESTED THAT WE MAY WANT TO MAINTAIN RADIO CONTACT/RADAR SVC WITH APCH EVEN THOUGH WE WERE VFR AND OUTSIDE OF CLASS C AND THEY WOULD BE MORE THAN HAPPY TO PROVIDE ADDITIONAL TFC SEPARATION. I THANKED HIM FOR THE INFO. I FEEL THAT IN HINDSIGHT; MAINTAINING TA'S IS THE BEST COURSE OF ACTION; BUT I ALSO FEEL ICT APCH COULD HAVE PROVIDED THE TFC SEPARATION FOR THE FALCON PLT WHO WAS IN CONTACT WITH ICT. WE WERE PERFECTLY LEGAL IN OUR AIRSPACE AND WITHIN VFR GUIDELINES.