After WW1 my great grandfather was a wireless operator for AWA and worked at Thursday Island and Broome off and on through the 20s and 30s.
Moving back to Essendon in the mid 30s he began to work at Essendon and his role grew into that of talking to aircraft, from what I was told he and another man were the first to fill this role as a dedicated profession. I understand that date to be mid to late 30s.
I cannot recall exact dates, the airways museum had the info when I last visited about ten years ago