Your current segment as it is won't work 100%. The reason is that you're using a Visit container that encompasses your Cart Additions and Product Name. That will match this scenario as well:
Hit 1: Added product X to cart. --> Cart Addition exists.
Hit 2: Viewed product "specific product name". --> Product View exists, Product Name contains any of "specific product name".
Hit 1 matches the "Cart Addition exists" condition and Hit 2 matches the "Product Name contains any of ..." condition. But the resulting data is not what you want: adding that specific product to cart.
So you need to nest your "Cart Addition exists" condition together with your "Product Name contains any of..." condition in the same Hit container.
Visit container:
- Cart ID exists
AND
Hit container:
- Cart Addition exists
AND
- Product Name contains any of ...
AND
(exclude)
Exit Cart Value equals 0