Open Atrium: How to add an action button on a view node
I found the solution. First, some terminology: the links in the dropdown menu on the bottom right are called Contextual Tabs. Second, the buttons with an icon are called Extracted Tabs. These settings are found in two different locations.

First, make your menu item a regular context tab. Go to admin/openatrium/setting and open the Contextual Tabs fieldset. Fill in the link to your page/menu item:



Next, extract the Contextual Tab as a button. Go to admin/config/user-interface/contextual-tabs and fill in the link and/or the label to your page/menu item in the Tabs to extract textarea:



Your link will now be displayed as a button with an icon of your liking.