It is blossom end rot (BER) and is due to a lack of calcium getting into the fruit.
Common causes are :
no calcium in the nutrient
reservoir temperature too high
not enough transpiration to move the molecules through the plant

Yeah, it's BER. Paste tomatoes are the most sensitive. And the first few tomatoes a plant produces will get BER the worst. Pick those damaged fruit and discard them if you haven't already.

That is a good point about a high reservoir temp possibly causing the problem.