I aw your website but could not find the floating widget anywhere. Can you please let me know once the widget is active with all the expected config set ?
Sometimes if you have any wordpress caching plugin enabled, then the plugin may have cached only the desktop version of the site. So when users from mobile visit they are served the desktop cache. If possible please do see if there are options to cache for desktop and mobile. This is because, the device is checked on the server side.