I also have a struggling Hinoki... though in my case I am sure I was too rough with the roots this Spring. It was badly pot-bound in nursery soil and I had to really hack at the roots, they were so dense. It looks similar to OP's now, but worse. I suspect it's not going to survive the Winter, but I'm not giving up until it's totally toast. Just praying, watering heavily, and keeping in dappled shade for now.
Another Hinoki I have that I was much gentler with and planted in a more moisture-retentive mixture is doing fine, even in full sun. They seem to like lots of water, even on the foliage. I hose down the whole plant daily and it couldn't be happier from what I can tell- lots of thick, vigorous growth all over.
I agree with Frank, they do not respond well to heavy root pruning or dry conditions. I think going forward I am going to incorporate more organic material in their soil mix, they seem to appreciate it. As long as they're not sitting in water all day (be mindful of perched water tables), I don't know that it's possible to overwater a Hinoki, especially in a primarily-inorganic substrate. I have seen it mentioned in other threads on this forum that one reason they are not very popular trees in Japan because they need much more watering than most other conifers do.
These trees love to drop older, interior foliage and back-budding is as rare as hens' teeth. In my experience, normal die-back usually occurs over Winter and is evident in Spring or early Summer. However, browning of exterior foliage typically indicates a problem- usually sun scorch or exposure to excessively dry wind that kills the foliage outright. If neither of these are likely, then it may be a stress response to sickness or injury. I think Mr. Hartinez is correct in that it's a delayed reaction to the repotting, hopefully not a total decline due to some other issue. The tree does have lots of healthy growth still, which is a good sign.
I'll cover the pot with a white cloth to hopefully cool it down.
I think that is a good idea. Next Spring, if the tree is healthy enough, you might be able to either move it to a deeper pot or lower in the same pot. In the meantime you could also consider top-dressing with chopped sphagnum moss to help keep the roots cool and moist. As it is they are very exposed and may be drying out too much.
Out of curiosity, do you know what cultivar this is, if any?