The problem is occurring when you convert to jpeg. To best avoid this sort of thing happening it is best to do all of your processing, resizing, etc. in photoshop with the 16-bit file. Then as a last step convert to jpeg and save. The higher "quality" setting you use when saving, the less artifacts there will be. Also don't modify the jpeg and resave it. Every time you save a jpeg it can create artifacts. Kind of like making photocopies of photocopies of photocopies of a document. It loses detail and gets uglier with each step.
Sometimes you get stuck with file size limitations required by websites and have to reduce the quality to be able to post. If you have done all of the above and reducing the quality to meet upload requirements creates the artifacts, well too bad. The technology has its limits.
Sorry for any appearance of testiness. But it was pointed out early in the thread that you were dealing with jpeg artifacts but you seemed to be fixated on it being a camera problem. Somewhat understandable I guess. When you spend $6k+ on a camera is seems like everything that comes out of it should be perfect