(Jetpack CCT) content-portfolio.php doesn't seem to get recognized

Hello everyone,
I’ve activated Jetpacks Custom Content Types and wanted to style the portfolio section in a different way than normal posts, so I created content-portfolio.php, content-portfolio-single.php and single-jetpack-portfolio.php

Viewing a single portfolio item works, however “content-portfolio.php” doesn’t seem to get recognized, instead it’s using the standard “content.php”. Thus the exampleurl.com/portfolio/ has the same style as the normal post section.

Is there anything I need to do in order for “content-portfolio.php” to get used?
I checked the source files of popular themes that support Jetpacks CCT like “Espied” and “Illustratr” but couldn’t find anything specific other than add_theme_support( 'jetpack-portfolio' );.

I’m happy about any hint that might lead to a solution, thank you!