If someone says “coming in the Spring” I literally have no idea when that is. The dates of seasons are meaningless.
Seasons are dumb. I remember reading a rant on the Internet once that advocated that we should recognize two seasons - summer and winter. You could put the boundary at equinoxes, with summer encompassing both traditional summer and spring, and winter encompassing traditional autumn and winter. The definition would be simple: summer is when it's kind of warm most of the time, winter is when it's kind of cold most of the time. I remember this resonating with me much more than the traditional definition.
Going back to temporal coordinates, the older I get the more confident I am in feeling that, for terrestrial use, anything that's not an ISO 8601 date is garbage and should not be used.
At least in the part of the US I'm from, we only used "Fall" for "Autumn", because colloquially it was already defined as a simple and pretty tight (but often slightly different each year) period: When the leaves on trees have changed color, but not yet all fallen off.
I'm similar to you, though I don't even have the excuse of living with different seasons - I just never really thought about it.