Looks like you have enabled the "Page Page Cache". It is only for static joomla website where all pages are static and no user interaction is occurred.
"Page Cache" is caching the full page and turns the page into HTML, then serve this static HTML until the cache-timeout is expired. So, once you add a product to cart and refresh the page, the old cached page (HTML) is being served so you still see ZERO. (actually the product is still in the cart, saved in the session, but you just don't see any indicator on the website)
FYI: "Page Cache" and "Joomla Cache" are different thing. Joomla Cache is caching only the objects, and reduces database hits while keeping the website dynamic, but "page cache" is caching the whole pages & everything and makes the website completely static.
First of all, open the "Joomla Plugin Manager" and search for this plugin: "System - Page Cache" and make sure it is disabled.
If that plugin is already disabled, then look if you have any other 3rd party cache plugin you have and disable them all. There are many cache plugins (JotCache, CacheControl), try typing the "cache" and search in the plugin manager.
The only enabled cache should be "Joomla Backend >> Global Configuration >> Cache", other than this, all other cache-related things (plugins or template settings etc..) should be disabled.
Regards