I believe we have discussed this through the priority support service.
For anyone else having the same question: featured images are only displayed in (posts) lists – blog, categories, archives, search results. On single post or page sections the images can be included in the content at the appropriate desired location.
Separately, the theme is capable of using the featured image instead of the header image – this requires the activation of a general header image and large enough featured images (the size condition can be disabled, though).