I repeat the question: when is the recalculation of related posts?
The answer to this is a little complicated, but here goes…
First off, it’s more accurate to say “recommended posts”, because post A can recommend post B, but post B might not necessarily recommend post A (whereas “related”, we realized, implies a bi-directional relationship.) Anyways, there are two stages to calculating recommendations: clearing the previously-cached recommendations for a post, and calculating the new recommendations for a post. They can occur together or separately.
Clearing the previously-cached recommendations FOR ALL POSTS happens when: (1) YARPP settings are changed or (2) when the “Empty cache” button is pressed on the YARPP settings page.
Previously-cached recommendations for an individual post are also cleared when you: (1) click the “Refresh” button you mentioned on a post’s editing page, (2) when that post is updated, or (3) also when another post’s recommendations are calculated and this post came up as one of the recommendations (eg, a new post was written that’s very similar to this one: in this case we probably want clear its recommendations because the new post should maybe become a recommendation for it.)
Calculating current recommendations happens on-demand when viewing a post’s recommendations. Ie, when (1) viewing a post on the frontend (and they weren’t previously cached), or (2) when clicking the “Refresh” button you mentioned (as you can see that button both clears the cache and immediately recalculates recommendations.)
So, the short answer: YARPP usually does a pretty smart job of clearing recommendations, and the problem I think you’re experiencing usually doesn’t happen. There’s something in your selection of plugins+theme+configuration that’s causing it to happen. So in order to figure that out, we need to gather some more information.
So first off, is this happening on a public website we can see? If so, can you please share the PUBLIC URL of your website, so we can see the problem happening? (That might help us identify the problem).