I am not aware of caustic soda is whether used for cleaning the salt. My current knowledge is that mainly water and more concentrated salt water is used to wash the mined or harvested salt for further cleaning and concentration. As the top heap after evaporation under sun is usually harvested, the major impurities get settled down . The harvested salt is further washed with good water or good concentration salt water to clean and keep the concentration and content. I am not aware of any use of caustic soda during the process. I am not able to understand scientific logic about mentioned use of caustic soda anywhere in the process. In fact caustic soda is manufactured by electrolysis of salt (sodium chloride).
Established manufacturers of iodised or common salt, are subject to quality control and they have to display the ingredients on the package label.Harmful chemicals are not allowed to contaminate the common salt used for food and human consumption.
However even if we extremely assume that there may be traces of caustic soda in the common salt we use, because of the minute quantum of salt we use the impurities also will be very very minute in quantum. Moreover, as cooking involves a laborious process of addition of various ingredients and water, even the minute quantity of caustic soda, if at all present, gets cancelled by coming into contact with various acidic ingredients added in the food.
However(for awareness), caustic soda, by itself is a corrosive strong alkali, and can create burning sensation and irritation like some acids. Many products we use are made using caustic soda as one of the ingredient. But because it has undergone chemical reaction during the process, we do not come into contact with casuistic soda as such in such products.