template_part not being caches

I have hyper cache installed and it’s creating the cached files in the correct location, and the cached files are being served up, but it appears that every refresh of the page is hitting my sql server still, which is most of the reason I needed to cache the pages.
The page in question: https://www.myconfinedspace.com/2017/09/27/superman-is-speedy/
below the tag cloud is a set of related posts that are being generated by a template page named related.php and I’m calling that page with get_template_part.

The browser cache settings are being set correctly, if you refresh this page several times, everything stays the same. However, if refreshed with a ctrl+refresh or loaded in a new incognito window, I’m seeing different images loaded up every time, which isn’t what I was hoping to see, as that means its hitting the database every time it loads.

Any idea where I’ve gone wrong?

The page I need help with: [log in to see the link]