It is a phenomenon called efflorescence which is simply the natural salts and minerals in the stone being deposited on the surface as water within the stone evaporates. You can try gently brushing it off on dry days but it will probably continue for some months yet.
We call it saltpetre here. Common occurence after tiling. To eliminate these salts, you just keep washing/rinsing with water only and mopping dry. Takes a while but it does eventually go.
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