These buttons inside Rey’s admin bar menu’s Refresh are meant for clearing or flushing various caches.
When publishing in Customizer, the styles generated by the controls will get stored in a transient in order to perform the site loading better.
To refresh this css you can either access Customizer and hit the Publish button, or just click on this button
Rey has an assets management system where component’s assets (CSS and JS) are split into tiny pieces and loaded only on demand.
If a Caching plugin is not enabled, Rey will merge all these assets into single compressed files.
This button will delete those files so that on the next page reload, they’re going to get regenerated.
This button deletes transients (cache entries) made by various Ajax requests (lazy loaded content, static data that’s usually the same for each visitor, etc.).
To prevent/disable the Ajax caching system from working, you can add this line
define('REY_DISABLE_AJAX_CACHE', true); in wp-config.php file , however do know that important savings are made with these processes.
If you’re just annoyed by the fact that you save something and the cache has not flushed for some reason, try adding that line only when you’re developing the site, but remove it once you’re ready to launch.