Hello,
Theme does not cache the header structure, only mega menu items and we use the default WordPress object cache https://developer.wordpress.org/reference/classes/wp_object_cache/
Description of your issue looks like cache issue. Maybe you have any server cache? Or maybe if you even disabled the cache plugin you still have cache enabled from the wp-config. So, provide us with WP Dashboard and FTP access to your site. And also contact your hosting provider and ask if they have any kind of server cache or cloud CDN with cache.
Regards