MY smaller satsumas are good eating. The peeling on the large fruit has a lot of white string material between it and the fruit. The fruit itself has very little juice and contains white dry material. Last year I had to throw the satsumas away. This year I water the tree all summer. All the big fruit are bad. The smaller ones are good. When it quits raining I can send pictures if you need.
The satsuma fruit segments in your picture show that they were sunburned. This is not uncommon on satsumas in general, but it is noticed more on young trees that have less developed canopies to shade the fruit as the sun moves across the sky. In very late summer, you will notice those areas on fruit facing the sky all day turn yellow earlier than the rest of the fruit. Those spots lose their ability to cool and then bake in the sun, damaging the inside of the fruit.
The big fruit you refer to are likely late bloom fruit. Fruit formed from the latest blooms are often large, thick skinned, have, pebbly textured peels and have lots of "rag" material---the white albedo tissue between the peel and segments. Late bloom fruit often sunburn as well, due to their shape and orientation.
You are doing well to continue watering. I also recommend that you fertilize the trees properly, especially in the years when they have a good crop. Trees that are not fertilized enough will not produce consistently from year to year, and produce more late bloom fruit.