How to pass arguments to add_action() [duplicate]

The parameter needs to be passed to the callback function in the wp_schedule_single_event function, not the add_action function.

Try this:

add_action('z_purge_products_cache', array($this, 'purge_products_cache'));

Then schedule the event, putting the parameter in an array:

wp_schedule_single_event(time() + 20, 'z_purge_products_cache', array($asins_r));

Your purge_products_cache function will be called with parameter $asins_r.