Hottest day of the year in the US varies by 3 months from California to Texas, which is only about half the width of the country. I would imagine the region you're in has a different hottest day of the year from say Kashmir or your neighbor Sri Lanka.
I don't know whether to call it a corner case or not, but I was pretty easily able to find this one (based on my own experience – the peak temperature in the East Bay has always felt very late in the year): https://weatherspark.com/compare/y/541~3268/Comparison-of-th...
Probably depends on where you are, etc., but as an European, I was taught in school two ways of splitting the year up into seasons: calendar/astrological and meteorological. Calendar split is based on solstices and equinoxes (21st March, 21st June, ...), whereas meteorological is based on month start (1st March, 1st June, ...). They use this also in weather reports, for example, where on 1st March they would add "Today starts meteorological spring" and on 21st March "Today starts calendar spring".