We chartered on owners time out of Dream Yacht Charters last year during the same time frame that you are going. The experience was fine, except that they had to exchange the Lagoon 520 we were supposed to be on for a Saba 50 due to apparent issues with the Lagoon. Those things happen I guess but it would have been nice to know ahead of time. Maybe because it was owners time it wasn't communicated to us effectively. The boat was well equipped and the check out and check in went without a hitch. We had one service call due to a bad fuel filter while we were motoring from St. Thomas into fairly rough swell. They sent someone out to meet us at Soper's and had it fixed within a couple hours. Overall, our experience with DYC was on par with other charter companies we have used (aside from the boat exchange which I consider an anomaly). We are chartering with them again this June but out of Antigua.
As far as conditions, we were there for three weeks. The first half was perfect 10-15 knots most days and small swell. I was expecting it to be super hot and humid but it wasn't bad at all. The second half the wind kicked up to 15-25 knots and 6-8' swell. While we enjoyed those conditions, it was a bit rough for a few people that were down with us. Nothing unmanageable by any means. Not sure if this is normal for June/July as I've heard the winds can get light, but it was great for us.
We were told that the second half of June can be like a mini high season as families come down once school is out. However, we found that with the exceptions of Cooper and Anageda, mooring balls were generally easy to come by well into the afternoon at most spots. Pretty much all of the bars and restaurants were still open but reservations were easy to come by and generally not even needed. It was nice that there were more boats with kids compared to other times we've gone that were not during a school break. We didn't run into any cruise ship crowds, though I know there were a few down there on certain days. Not nearly as many as winter and spring time though. Not sure which schedule to look at to determine when they will be there.
All-in-all, we had a great charter and I wouldn't hesitate to use DYC, or to go at the start of summer again.