Content Fragment model display mode not visible in Editable Template

We have an Editable Template that includes a Content Fragment component.

The Content Fragment component is configured to reference a placeholder content fragment model. The display mode is selected.

I do not see the display mode take effect in the Editable template.

If I add a Page using the Editable Template, however, the display mode has taken effect - and I see the content (from my Content Fragment) and the page structure/layout (an outcome of the Display Mode).

Here is the editable template -- which includes the Content Fragment component in the initial content.

Here is the page -- where the display mode is active. 

The issue I am trying to solve: 

I want to include initial content in the right rail.

But, the right rail is not accessible at the template level.

As an outcome, a content author must manually author components at the page level -- rather than those components being included in the initial content of the editable template.

What am I missing? Is this a change that can be effected by Content Authoring? Or would this require a code change from our development team?