After doing further research, it seems that is exactly what happened.
Mix 106.5 Sydney replaced their original purple/green/pink logo with the blue/yellow/red one in May 2001, not long after several on air presenter (David Rymer, Trevor Sinclair and Rob Duckworth were out while Jason Bouman, Mardi Cole and Solomon Gates were in - Bogart Torelli and of course Richard Mercer kept their timeslots) and behind the scenes changes:
Full article/page is available via Newspapers.com, for anyone interested.
Anyway…it’d seem likely that ARN had the wheels in motion for the station launches/rebrands in other markets (with 106.5 Sydney, 101.1 Melbourne, 97.3 Brisbane, 102.3 Adelaide and later 106.3 Canberra all having their own version of the blue/yellow/red Mix logo) as far back as May 2001, if not earlier. Certainly the Sydney, Melbourne and Adelaide stations all had their own slightly different versions of what was essentially the same television commercial with the audio equalizer-esque logo animation:
Screencaps of the Melbourne & Adelaide TVCs were taken from commercial compilations on YouTube uploaded by MOARPSYK and GreenYoshi93 respectively, so full credit to them for those! 
I’m not so sure whether there was a 97.3 Brisbane version of that commercial, however they definitely had versions of the “Songs that say something” TVCs which were running about a year later:
Yes I know the formation of the Mix Network and their associated ad campaigns during the Early 2000s isn’t something many of Media Spy’s radio enthusiasts are likely to look back on as a good thing for radio (especially since it resulted in the demise of local brands TT FM and 5AD-FM) but at the same time, I hope my write-up about this branding has been an interesting read all the same!