The Custom Twitter Feeds plugin should work in compatibility with most, if not all, caching plugins, but you may need to tweak the settings in order to allow the Twitter feed to update successfully and display your latest posts.  If you are experiencing problems with your feed not updating then try disabling either ‘Page Caching’ or ‘Object Caching’ in W3 Total Cache (or any other similar caching plugin) to see whether that fixes the problem.
You can also try enabling the Force cache to clear on interval option in our plugin by following the steps below.
- Go to WordPress Dashboard > Twitter Feed > Settings > Advanced
- Enable Force Cache to clear on interval
- Click Save Changes