Hi, live in Japan and have been growing tomatoes (no idea what type because I wasn't able to read the seed package—but, they grow like indeterminate tomatoes, the tomatoes grow close together, and larger than cherry tomatoes) on my 4th story porch.

None of the fruit has been affected or show signs of any problems at all, just the leaves. Mostly the ones on the lower half of the plant at first, but now some of the newer growths and higher up leaves have ...well you'll see it in the picture. After a few days with whatever is on those leaves, they'll shrivel and die. So far I've just been cutting off all affected parts of the plant.

Additional info:
Some of my pepper plants have spider mites and I've treated them for that, but whatever this is on my Tomato plants I haven't been able to figure out and treat. The color is much more orange than spider mites on the other plants. If they are pests, they're smaller than spider mites and I never see them move. So, disease? Please help.

They are indeed spider mites: some species like tarsoneme are pretty much invisibile to the naked eye and you only get to see the damage, but in your case the masses of droppings, exuvia etc at the leaf tip are diagnostic, as is the leaf curl.

I don't know what you have available in Japan, but spider mites are very tough, hard to get rid of pests. If you cannot get a miticide (or a double action insecticide/miticide) or don't want to use it, get some agricultural mineral oil and spray your plant throughly with it, then repeat the treatment after a few weeks to be sure to kill any eggs you may have missed.