Oh, I have never heard of seasons starting mid-month. My mind is blown!
In Australia it's just split up by months, with each season being 3 months long:
March 1 - Autumn starts June 1 - Winter starts Sept 1 - Spring starts Dec 1 - Summer starts
Of cause, those in far northern Australia, only really have Dry and Wet seasons. I have no idea when those are.
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...
Part of the reason for this is that climate lags behind sunlight a bit, so the end of the authors "summer" would be warmer than the beginning.
But most countries other than the USA use meteorological definitions of the seasons starting on the 1st of December, March, June, and September.