when I clean from joomla's backend, the entire content of /www/cache folder is correctly deleted.
but when I use secret url to clean cache from the website front-end, only the page folder is deleted inside /www/cache folder, see here :
This is probably because the page itself creates new cache while rendering, after Cache Cleaner is done emptying the folder.
Check if the folders/files are all from the time you load that page. That means all older cache has been correctly deleted.