[Plugin: W3 Total Cache] No Page Cleanup Past Homepage After Disabling WP-Cron

I have disabled wp-cron by adding the line define(‘DISABLE_WP_CRON’, true); to wp-config.php. I then added a crontab entry to invoke wp-cron.php using the php command. Everything is working as expected with the exception of W3TC. When my client publishes a post, the last post on the homepage is pushed off as expected. However, it does not appear on the next page nor are the rest of the posts pushed back. If I empty the page cache, the post in question appears where it should (the first post on the second page) and all other posts are pushed back.