Thought I'd give an update. I had lots of difficulties starting the seeds in the rock wool. I've never grown much from seed before and it is a learning curve. I finally got 3 plants large enough to move to the buckets and by that time it was January or February, not a great time to start tomatoes here. They are doing great so far, there are even tiny tomatoes on them.
I put up the sun sail this week because they were looking kind of stressed in our spring heat, it was over 100°f for about a week. It has cooled down this week and we had a heavy rain. I'm worried about the heavy rains of summer as well as the heat so I thought a bit of shade and rain protection was in order. We'll see.
The hydroponic part seems to be working well, I upped the frequency and duration of the pump during the hot spell so that they were getting the solution on their roots for an hour and a half and then off for a half hour all day. I may reduce the duration now that it is cooler and they have some light shade.
I don't know why some of the leaves are curled. I have cut off some of the lower branches without blooms but I really don't know what I'm doing. I'm open to pruning suggestions and I am going to go and do some googling as well.