WooCommerce Global Cart works great on mobile devices using Safari browser
Safari browser is well known for it’s cookie policies which is in a way a nightmare for developers to implement specific features. It has defaults that are arguably more secure than other browsers, but this winds up breaking some techniques mainly used along creating crossdomain cookies.
The sessions that any decent website relies on, do not work ( e.g. users not able to login, etc), as the session cookie is not ‘trusted’ by the Safari browser. Per Safari Developer rules, a domain which has not been visited in a session, it will not save any cookie created for it.
The WooCommerce Global Cart plugin use a special functionality to make this functional, following the exact guidelines and safety measures proposed by Apple. This is achieved through a transparent and interactive Synchronization procedure, which acknowledge the browser and the user upon the domains that need the required cookies.