These detailed steps are for Xcode 4.6.3 but should be very similar in Xcode 5.
1. Add a view controller to the storyboard of the desired type (ex: View Controller). [Drag from the Object Library.] I think you have already done this.
2. Create a class module for the view controller. [File > New > File... > User Interface > iOS > Cocoa Touch > Objective-C Class.] Specify an appropriate class name (ex: FirstTabDetailsViewController), subclass from the same type used in step 1 (ex: UIViewController). Do not check XIB.
3. Select the new view controller in the storyboard. Be sure the view controller is selected, not the view. Easiest way is to select in the Document Outline, not the design surface. In the Identity Inspector > Custom Class > Class, select the class name of the class you just created.
4. Build to confirm everything is hooked up correctly.
5. When you show the assistant editor for the storyboard, the new .h should appear.