I suspect your cups are not very old. I could not find a listing on Tiffany's website.
I suggest you watch eBay's completed auctions for a value. I recommend you watch for at least a month. I did a quick search and saw that a single smaller cup did not sell for the initial bid of $27. A large gilded cup sold for the $125 initial bid. I doubt if the double strike is considered a rarity that would add to the value of the cups.
Jefferson cups have been reproduced for years and are still being offered for sale by several retailers. The larger cups seem to retail for approximately $200. Your cups are smaller and as you suspect may be used as salts.