First cache preload does not preload custom post types (if you use it!)
Than better to use external cache preloader as script below setting it on your linux server as CRON job:
#!/bin/bash
#
# This script reload all the cache on web
#
CACHEDDOMAIN0001="example.com"
WARMLY_REJECT="gif,jpg,jpeg,png,pdf,txt,xml,ico,svg,css,js,json,eot,woff,woff2,ttf"
cd ~/web/${CACHEDDOMAIN0001}/public_html/
/usr/local/bin/wp super-cache flush;
cd ~
#rm -R /home/admin/web/${CACHEDDOMAIN0001}/public_html/wp-content/cache/supercache/${CACHEDDOMAIN0001}/
# --- what's about --no-cache parameter???
# Fetching desktop version
wget --content-disposition --reject-regex "wp-json|wp-includes" --reject=${WARMLY_REJECT} --spider -o wget-${CACHEDDOMAIN0001}.log -e robots=off -r -l 5 -p -S --header="X-Bypass-Cache: 1" ${CACHEDDOMAIN0001}
# Fetching mobile version
wget --content-disposition --reject-regex "wp-json|wp-includes" --reject=${WARMLY_REJECT} --spider -o wget-${CACHEDDOMAIN0001}.log -e robots=off -r -l 5 -p -S --header="X-Bypass-Cache: 1" ${CACHEDDOMAIN0001} --user-agent='Mozilla/5.0 (iPhone; CPU iPhone OS 8_0_2 like Mac OS X) AppleWebKit/600.1.4 (KHTML, like Gecko) Version/8.0 Mobile/12A366 Safari/600.1.4'
# Deleting temp wget directory
rm -R ./${CACHEDDOMAIN0001}
