You're describing cache maintenance (and cache eviction), a practice for which there are many algorithms (FIFO, LRU, LFU, etc.), including the algorithm the article describes (SIEVE)
I think this is orthogonal to cache maintenance and cache eviction. Instead this is having a background process periodically refreshing the data in the cache to keep it hot.
Refreshing the cache to keep it hot, and deciding how to do it, e.g. which parts do we do with the caching layer directly, which parts do we do with an external process, what to evict to make room, etc, are subtopics of cache management.
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"