This may be a bug report. I have detailed the circumstances in the Cities Skylines workshop discussion

In short:

I believe the Steam client implement HTTP caching for Workshop mod files, and the URL for the individual files does not contain a release tag.

This causes mods which are updated, while keeping filenames unchanged in the "new" version, to use a previously downloaded, cached (stale) version of the updated files, instead of the freshly pushed updated files, since the URL for the new and old files is the same, and cache freshness heuristics reasonably skip cache revalidation.

A workaround that works for me is to rename the updated DLL filenames to include the updated version. This forces the Steam client to consider downloading a file which cannot possibly exist in its cache.