I have literally never heard this, and I’m more aware of the vagaries of USA and European business and general practices than most others in Australia.
If someone on the internet says “Spring 2022”, I immediately assume it’s speaking of northern hemisphere temperate regions’ spring (because such dating is uncommon in the southern hemisphere to begin with and never used in public/worldwide internet situations because we’re more aware of these things), and after thinking carefully for a bit to straighten out in my mind when that actually is, I assume March–May 2022 or possibly a week earlier (equinoxes and such), because that’s what would be meant in Australia, if we ever expressed things like that (apart from the whole off-by-six months thing!). I would not expect June to be reckoned a part of it any more than I would expect March to be a part of Q2.
(Incidentally, a year or two back I heard suggestions that “Q2” may customarily be anchored to financial rather than calendar years in some places. Not sure if this is true.)
If by “spring” you meant to convey “the second quarter of the Gregorian calendar”, you failed to communicate accurately.