In some ways, caching can be seen a prediction problem. And the cache hit rate is the error as we lag the previous history at time T. Blending load over time is effectively what these various cache algorithms do to avoid overfitting.
Tho potentially just refreshing out of date data in the cache could increase effectiveness given that general assumption of the cache is whats in the cache will probably be used again.
I called it a periodically refreshing cache when I wrote one. Not sure if there is a more formal name.
If I understand you correctly, you're asking if this is different because an external process is involved. I don't see a use in drawing a distinction, and as far as I know, there's no special term for that pattern.
Update: after looking into it, it looks like this cache/architecture pattern is called "refresh-ahead"