The coloring solids left behind are larger particles than normally used
in a finish which allows them to go on so unevenly and out of
suspension (as opposed to paint). The particles are usually some kind
or ceramics or in the case of others, some kind of metallic oxide.
At any rate, they are more pourous and will attract the oils, etc. at a
different rate than the areas with less "pickle". This will then make
the finish uneven. Then, the chemical reactions between the finishes
(and in some cases the pickling agent has no finish at all and is
considered a "treatment") will cause the yellowing.
I personally don't think this is fixable. If you refinish, there are
some great waterborne finishes out there to try again.