Sometime shortly before that date, Season 20 will end.
The reason being, is that quote above is talking about a patch update to D3. And its VERY likely it will be a larger patch, which may include this password change they are talking about here where I quoted that from:
But the point I want to make, is why would a passwording update require them to wait till June to apply it? Why wait when the rest of the system was updated already this month?
Simple. Its easier to roll it in with the next game update, which will likely include the Season 21 changes. So expect the new season to start at 5PM Pacific time on June 12th, and this season (20) to end the Friday prior, June 5th. With the June 9th update to fall exactly on a Tuesday, which is a typical day for Blizzard to do maintenance.
But that’s just me.
Game on.