@JustinFromRelias If you are using the script mentioned in https://adobe-consulting-services.github.io/acs-aem-commons/features/redirect-map-manager/index.html
The user which would execute the corn job to import the redirects from publish to dispatcher instance should have.
execute permission for /etc/cron.hourly
write permission for /etc/httpd/conf, /var/log/httpd, /tmp