For myself, it does help with hydrating the under eyes after application. I have trouble sleeping as well and often have dark circles because of it. I've actually noticed that using this both in the morning before my spf eye cream and as my eye cream before bed, my under eye area has improved a lot.
This product does give a cooling sensation under the eyes but that is all I got out of it. I have not noticed a difference. It does do a little bit of moisturizing. I would not buy this for dark circles or under eye bags.
I don't know about their brightening stick (which is a different item), but I love this as a way to de-puff my eyes. It smells great and I feel like my skin is calmer, less puffy, and softer when I use this product.