Before COVID-19, INSEAD started sending interview invites about 10 days before the notification date stated on their website, and most (not all) rejections were sent out on that same notification date. So, some applicants received their rejections a few days prior to then.
But COVID-19 has changed everything so, we don't really know what is going to happen this time. For example, one of my R2 clients got her interview invite on June 6th, so quite early by "INSEAD standards".
This year, INSEAD has received an unprecedented high number of Round 2 applications so, please just wait patiently for the emails to come. I know it's easier said than done, though.
Good luck to everyone!
Warm regards
Alex