We were taught the same (Australian) - though it always felt slightly off as March often has major heatwaves, and December can be quite spring-like, often cool and wet.

Adelaide’s climate anecdotally feels to be more humid in recent years (historically bone dry Mediterranean climate) and the seasons feel like they’ve shifted a few weeks forward.

The Kaurna (Australian Aboriginal people of Adelaide, pronounced Gar-nuh) apparently mapped seasons a little differently, with a longer summer that resonates with my experience:

https://www.bom.gov.au/resources/indigenous-weather-knowledg...

The Noongar people of Western Australia have a 6 season model that also maps pretty well to my experience in South Australia.

https://australiassouthwest.com/six-seasons-of-the-south-wes...