It would be useful to have a different colour or small banner next to the user account so that they know the access type they have when they are looking at a product. If the user hovered over that banner or their profile a link or pop out could appear which tells the user what they are able to do in this product.
I have Users confused about their permission options too. It is based on Workspace. So, it would be helpful for them to know what they can do. At least between the standard Contributor and Reviewer.