Yes, sounds like a caching issue. There are two possible points at which this can happen.
Persistent object/database cache via W3TC, etc., which should be cleared when the post is updated.
Browser cache, which again, could be coming from W3TC, etc. or from your .htaccess file putting expiry headers (or related, via a proxy cache, if any).
The plugin places the proper last-modified header on the file before serving ( https://github.com/benbalter/WP-Document-Revisions/blob/master/wp-document-revisions.php#L752) , but perhaps a revisit of the expiration is in order?
The original code was taken form
ms-files which was designed to serve static files. It's hard to say what the expires header should be. It sounds like your use case is updated frequently while others may update rarely if ever. I believe this would be best implemented as a filter.
I've created a issue on GitHub to track the feature. https://github.com/benbalter/WP-Document-Revisions/issues/38. Pull requests are always greatly appreciated if you are able to take a stab.
For the time being, linking to the specific version of the document (e.g., ?revision=X) or apending a query string (e.g., ?break_cache=1234) should solve the problem until the plugin is updated.