The other seasonal events coincide with seasons of the northern hemisphere so I don't see why they would postpone the summer event but leave the others be.
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If we're getting the speculated yukata, then I would guess the summer event to possibly coincide with Japan's O-bon festival which doesn't start until mid-August. Lots of cute girls wear yukata during O-bon, so it seems appropriate to me!
I think it's likely to be in 2-3 weeks. Thats just my guess though. ARR launched end of august iirc last year, and they had the summer event 1-2 weeks after. It was later than it had been previous years but they wanted to fit it in there so new players wouldnt have to wait a year for the swimsuits, so if the game hadn't been down it should have been before the end of august
Japan, I believe, also considers summer to start when the hot rainy season ends. So it's not really summer until the rain stops.
And yes in the old Japanese calendar, summer was from early May to early August.