Feeding outdoor tomatoes

The greenish in the water is unlikely to be nasty, it is the excess water itself that might well rot the roots.
Plants in pots here all have a way out for excess water. I wouldn't dream of lining with plastic. As long as the compost isn't allowed to dry out, any running through is in excess of what the compost can hold and needs to escape I would have thought.

I have found Dalefoot composts to be very good - but expensive. They advertise on their web site that plants don't need additional feeding and have a mix for tomatoes. If you have a supplier nearby you could give them a try. Whether the savings on feeding would balance the extra cost of the compost?
https://www.dalefootcomposts.co.uk/our-stockists.aspx

I bought it to see what it was like as i have a patch of bracken near by and that is one of their main ingredients besides wool - but I didn't get round to cutting it this year, may be next. In mid summer with 101 things needing doing, next years compost making is easy to miss.