Issue where SharePoint users see an old unsynchronised Word file

The issue is that users open a Word document from a shared library into the desktop app, only to find that:

1. There's no Autosave feature enabled in the top-right.
2. The document version label we add on the frontsheet shows a very old minor version.

I believe also that the file is read-only, and the only option they see is to save a local copy and upload it back to the library; which is not good practice since it's an old version.

They report that the issue is resolved after exiting OneDrive, and deleting a Local cache folder. Has anyone experienced this issue and know what to try?