Just picked this thread up.like Pemba I have fixed thousands of mts moleanos over the years.
a number of good points have been made but I will repeat what I have found from my experience as not only a stone fixer but also stone restorer.
i have seen this patchiness many times.it is far more common when stone fixed with non rapid flexible adhesive.
the moisture migrates through stone bringing minerals from stone and polymer from adhesive to surface of stone. Water Moisture evaporates and leaves a stain on surface of tile.this has a slightly furry feel when compared to the surface of an unfixed tile.provided that all the moisture has worked its way out which I'm sure it will have by now,I would get a tin of lithofin wexa cleaner..mix a bit of wexa a 1:5 with water .apply with a sponge,keep wet ,don't let it dry in .scrub with bit of nylon pad and wash off.take a hair dryer and dry the cleaned part.best to try to halves of two different tiles to compare against a half not cleaned.
this works virtually every time.
rapid set adhesive should have been used as it would prevent this migration through stone as rapid set pulls moisure within itself.
i used to get a problem like this probably 15 years ago,when no one really understood about having to use rapid set.
I was using Ardex x7 slowset and ardion 90.i would solid bed stone but get a horrible yellowish stain all over tile.it would take as long to get rid of staining as laying the floor.
eventually I tried many different adhesives until I found weber stone set range.they had a slow set which by luck more than design did not stain stone.
i worked closely with weber rep and their chemists on this.
i then changed again when needed stone to dry quicker and now only use rapid.
The dark patches on your stone are where back of tile is in contact with adhesive.
the light parts are where there is no adhesive connected to back of stone and voids.
this patchiness is not seen on most limestones when you fix with slow set flexible.
its mainly moleanos,Turkish porous white ,apple stone and other solar stones.
give wexa a try. Would be interested to know if it works orm by all means call me