Since you can't see exactly what a customer sees when viewing the design area, this article will be your guide so you know what your customer's can and can't do in their own design area. Even while using the Design As User feature, you'll still see more options than your customers will see in their won design area so please don't confuse the options you'll see with the options they'll have access to.
The main menu
Customers cannot create new templates. They can only load the templates in their account and save them. In the main menu (the menu that's in the top blue bar), Your customer's will see a Save button when they have a template loaded. Along the right side, they'll see the download options, as well as their Avatar (to edit their profile) and a Help button.
The left menu
Your customers will have access to the following menu items.
Templates, Text, Backgrounds, Images
As you can see, this is slightly different than the menu items you'll see. Customer's do not have access to the Elements pane. Also, there is an Images pane that customer's do have access to. This is their area to upload and manage any of their images.
Customers can see most of the design tools. They'll see all of the stock fonts as well as any fonts you've added to your account. They cannot, however, unlock any items that you've locked. Customers can only unlock items that have been locked with the Position Lock feature.
Customers cannot adjust the size of their templates.