"Manage display" tab missing in Manage fields window
The tab might just be somewhere else. When you edit a content type, you see at least two tabs (provided that the core "Field UI" module is enabled):


Manage Fields
Manage Display


If you go to "Manage Fields" and then click on "Edit" for a given field, you will see the "Field Settings", "Widget type" and "Delete" tabs, as you say, but not the "Manage Display" tab. To see it, you need to go to the content type edit screen, it will display the list of fields and their display properties.

Hope that helps,