The only thing I see missing here
It appears that you are ordering a product and checking out, logging out and then ordering another product and the coupon code is working. This isn't really what I'm implying in the this problem.
I only have one product associated with a coupon code. The second product that shows up in the product page doesn't have an associated coupon code. I'm sure I did this right if the code works properly. I search products by selecting category "paper products" and the add to coupon on only the first picture not the second. That should associate a coupon code with only that single product. I then update.
If you go in and order two products in the same session, adding the first product with the coupon code associated first and then continue shopping and add the second picture without a coupon code and look at the discount it increments to $00.02 and reflects a discount applied to both products in the same cart. This is where the problem lies. It's discounting the second item added to the cart when there is no coupon associated to that product. It should only discount the one picture. If you can see the screen grabs I uploaded it shows that. Right now there is only on picture associated with one coupon code and only one coupon code in the store. Doesn't sound like you were doing two products in the same cart.