AN IFR SMA DEP DOESN'T FLY ASSIGNED HDG NOR ACKNOWLEDGED FOR FREQ CHANGE RESULTING IN LTSS WITH AN SMT ARR.

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I WAS SUPERVISING IN AVL TRACON. RWY 34 WAS IN USE WITH VISUAL APCHS. TFC WAS BUSY. THE CLOSEST ARR WAS CGA X AN SMT ON R BASE TO RWY 34. THE RADAR CTLR COMMENTED; WHO IS SMA Y? SMA Y'S TARGET HAD JUST APPEARED AND TAGGED ABOUT 1/2 MI SE. (BECAUSE THE RADAR ANTENNA IS LOCATED E OF THE RWY ON THE ARPT; E DOWNWIND DEPS DO NOT APPEAR UNTIL THE ACFT IS 1/2 TO 1 MI FROM THE ARPT). THE TARGETS PASSED APPROX 1 MI APART. THE LCL CTLR ADVISED THAT HE HAD BOTH ACFT IN SIGHT; AND THE CGA X PLT ADVISED THAT HE SAW THE SMA. IFR AND VFR DEP FROM AVL ARE ASSIGNED RWY HDG FOR SEPARATION PURPOSES. THE LCL CTLR TOLD ME THAT AFTER SMA Y HAD DEPARTED; HE INSTRUCTED THE PLT TO CONTACT DEP CTL. THE PLT DID NOT ACKNOWLEDGE; BUT WHEN HE OBSERVED THE ACFT TURN OUT; THE LCL CTLR BELIEVED THE PLT HAD CHANGED FREQ AND HAD BEEN INSTRUCTED TO TURN BY DEP CTL. HOWEVER; SMA Y HAD NOT CHANGED FREQS; AND HAD TURNED ON HIS OWN. (DEP CTL ATTEMPTED TO CONTACT THE SMA WITH NO RESPONSE; AND LATER WHEN LCL CTL CALLED THE SMA; HE WAS STILL ON TWR FREQ). I BELIEVE THIS SITUATION OCCURRED AS A RESULT OF SEVERAL EVENTS: LCL CTL DID NOT ENSURE THAT SMA Y HAD RECEIVED THE INSTRUCTION TO CONTACT DEP CTL; AND THE PLT OF SMA Y DID NOT FLY RWY HDG AS ASSIGNED BY GND CTL.