I'm not a tiler, you may want to try the tiling section here at BV too.
My guess would be it's acting like a vapour barrier.
Any place where you have cold meeting warm air you'll get condensate, that is when airs water as a gas state (vapor) meets a cold front will turn to a liquid state you know like morning dew.
You've probably heard of vapor barriers which is a sheet plastic between the warm & cold in a wall system.
Your tile being on the arm side is meeting the cool air and creating a dew type effect. Insulating the floor, and placing a vapor barrier on the proper side south & north are different you may be able to stop the reaction?
BUT, that is just an educated guess, have a local insulation conmtractor check it out and like I said try the tiling section too. ;)
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