I think it is reasonable to assume that the intent of the wording is to be day of departure from that particular airport. So you can use the SYD lounge on the day you are departing from SYD.
I understand that the actual text does not say that and a lawyer would walk right through it in court, but I do believe that is the intent and the way that Qantas Club staff will interpret it. So if you want to use it as an arrivals lounge, be prepared to argue your point and be prepared to loose the argument on occasions.
And yet I've never had a single problem (even at MEL DOM) showing my BP on arrival and saying "my lift is running late, okay if I wait in here" and being told that I am entitled to access.
If MEL DOM is prepared to allow it, then it MUST be so, we all lknow what they are like down there!
Dave