Content Templates modify the content when called from the WordPress’ built-in the_content function. Some themes do not use the_content function, but define their own function. In this case, Content Templates are not applied to selected posts on the front-end.
To solve this, you can enter the name of the function your theme uses on the Toolset->Settings page, under the Front-end Content tab. You can find the appropriate field in Theme support for Content Templates section.
If you don’t know the name of your theme’s function, check the Enable theme support debugging option and click Save.
Now, go to a page that should be displayed using a Content Template and copy the call function name that Views displays. Go back to the Front-end Content tab in Toolset Settings and paste the name of the function into the Theme support for Content Templates section.