just to be clear, pickling lime and kalkwasser are the exact same thing.
the reason you don't want to expose the kalk mixture to air is, the carbon dioxide in the air will diffuse into the solution, then it will cause calcium carbonate to form. this is the white precipitate that you see.
Also, if you dose it into your tank too fast, the carbon dioxide already there (not to mention any calcium and carbnates already in your water) will cause precipitation. The exact rate of dosage will be highly dependant on the chemistry of your water at the time of dosing, wether or not you add acid to the kalk mix, and how much CO2 is in your air. slower is better ime.