Shows old hompage

Did you use the debug log in the plugin to see what the plugin is doing when you look at the homepage? Same with updating a post, see if it is deleting the homepage cache.
Did you ftp to your site and look in wp-content/cache/supercache/youdomain.tld/ for the cache files? Do they match the time shown on the site?

Yes, I’ve checked the debug log but I don’t know what exactly I should look for.

I’ve deleted all files in the cache folder but same problem.

Unfortunately I can’t tell you what’s wrong. The debug log will however, but you’ll need to examine it carefully. It will say it’s serving a file, or deleting a file and sometimes why it doesn’t delete a file.

/wp-cron.php?…. GC flag not found. GC will go ahead..
/wp-cron.php?doing_wp_cron=… wp_cache_gc_cron: Set GC Flag.
/wp-cron.php?doing_wp_cron=…. Cache garbage collection.
/wp-cron.php?doing_wp_cron=… Cleaning expired cache files in …
/wp-cron.php?doing_wp_cron=… Doing GC on supercache dir: …
/wp-cron.php?doing_wp_cron=… prune_super_cache: did not delete file as it wasn’t a directory or file and not forced to delete new file: ABSPATH/wp-content/cache/supercache/index.html
/wp-cron.php?doing_wp_cron=…gc: could not delete ABSPATH/wp-content/cache/supercache/index.html as it’s protected.

That’s ok. Your website should be cached in wp-content/cache/supercache/domain.tld/ and the cache files will be index-https.html and index-https.html.gz probably.

… wpsc_is_caching_user_disabled: false
… wp_cache_get_cookies_values: return:
… wpsc_get_realpath: directory does not exist – ABSPATH/wp-content/cache/blogs/archives/
… wpsc_get_realpath: directory does not exist – ABSPATH/wp-content/cache/blogs/archives/meta/
… supercache dir: ABSPATH/wp-content/cache/supercache/…
… No Super Cache file found for current URL: ABSPATH/wp-content/cache/supercache/….
… wp_cache_get_cookies_values: return:
… In WP Cache Phase 2
… Setting up WordPress actions
… Created output buffer
… wp_cache_get_cookies_values: return:
… wpcache_do_rebuild: doing rebuild for ABSPATH/wp-content/cache/supercache/…
… wpcache_do_rebuild: exiting as directory is not a directory: ABSPATH/wp-content/cache/supercache/…
/wp-cron.php?doing_wp_cron=…wp_cache_get_cookies_values: return:
/wp-cron.php?doing_wp_cron=… In WP Cache Phase 2
/wp-cron.php?doing_wp_cron=…Setting up WordPress actions
/wp-cron.php?doing_wp_cron=…Not caching wp-admin requests.
… wpsc_is_caching_user_disabled: false
… Output buffer callback
… wp_cache_get_cookies_values: return:
… Anonymous user detected. Only creating Supercache file.
… wpsc_is_caching_user_disabled: false
… wp_cache_get_cookies_values: return:
… Writing non-gzipped buffer to supercache file.
… Renamed temp supercache file to ABSPATH/wp-content/cache/supercache/…
… Sending buffer to browser
… wp_cache_shutdown_callback: collecting meta data.
… Did not write meta file: meta-wp-cache-….php
supercacheonly: 1
wp_cache_not_logged_in: 2
new_cache:1

/?wordfence_lh=… https://…/?wordfence_lh=1&hid=… – Page not cached by WP Super Cache. Blank Page. Check output buffer usage by plugins.
/?wordfence_lh=… No closing html tag. Not caching.
/?wordfence_lh=1&hid=… https://…/?wordfence_lh=… – Page not cached by WP Super Cache. No closing HTML tag. Check your theme.
/?wordfence_lh=…wp_cache_maybe_dynamic: returned $buffer
/?wordfence_lh=… wp_cache_shutdown_callback: No cache file created. Returning.
/?…wpsc_is_caching_user_disabled: false
/?wordfence_lh=… Output buffer callback
/?wordfence_lh=1&hid=… Buffer is blank. Output buffer may have been corrupted by another plugin or this is a redirected URL. Look for text ‘ob_start’ in the files of your plugins directory.