More information about these cancellations could be found in J. C. Smith's "The Postal Cancels of Brisbane, Sydney and Perth" [1991]?
A review of this publication mentions the following:
"For those unfamiliar with these dies, they are primarily square and bear wording such as POSTED CITY BOX, POSTED PILLAR BOX, POSTED IN PILLARS, POSTED IN COUNTRY BOX, POSTED OVERSEAS BOX, POSTED IN CIRCULAR BOX, POSTED INTERSTATE BOX, POSTED AIRMAIL BOX and POSTED IN SUBURBAN BOX."
http://www.stampprinters.info/plb19.pdf