Products are searchable even if not in customer role

I have products that I have set up by category.  The category is assigned to a customer role.  I do not want my customers to see products that are not assigned to them.  When I search for a product, even though the category is not viewable by the customer, the product will still come up in a search.  Is there any way to stop this?

I also need a resolution to this problem.  I have a completely private shopping site.  Certain groups of customers are restricted from purchasing certain groups of products.  They can still find and purchase these products if they use search, or click a product tag.