It probably stems from the days when HK did not have full radar coverage over it's airspace (bearing in mind, HK provided ATC service as far south as Vietnam airspace after the war until 1999).
Althought the procedural separation was provided by a controller in the ATC Centre, the radio communication was normally via an HF operator with the callsign "HK Radio" if my memory serves me correctly. The Aeronautical Mobile Operator would relay any requests of change of level etc to the controller and they would repeat verbatum whatever the instruction given.
Once within radar coverage, the aircraft would be instructed to contact "HK Radar".
Granted, others such as Manila do not have full radar coverage but still call it "Control". It was the same in Australia. Must be a 1950's Pommie thing. Much of what we do is still rooted in that.