I deploy this site (which runs on Kirby, in case you didn't know) via DeployHQ and it has proven super helpful. I'm really happy with the setup, since I didn't want to move hosting, due to more than just one reason.
To make sure all the changes after each deploy appear on the site immediately, I run this short SSH command after each an every update to the site, which deletes the complete “pages” cache, leaving other caches, e.g. from plugins, intact.
rm -rf /path_to_kirby_installation/site/cache/domainname.tld/pages
This way I can be sure that all updates are visible on the site right away and no outdated pages are served.