The fourth batch, I believe that is what we are up to now, of notices that sites have been moved over to the mobile-first index has gone out over the weekend. I received a number of notifications over the weekend, like the previous batches, none of the sites I saw moved over were actually mobile-first – but we explained why that is the case over here.

If I had to date these batches, they would be on these dates:

March: Batch one was a small subset back in March
April 30, 2018 – was the second batch, but was way more wide spread
May 17, 2018 – was the third batch of notices
May 27, 2018 was the fourth batch of notices

Joost de Valk from Yoast noticed a number of sites getting this fourth batch of notices as well:

Here is the message from the fourth batch:

Forum discussion at Twitter.