I can answer this for you as I have been using CloudFlare for 3 + years now.
Yes, with the use of CloudFlare you now have in fact two caches. One at CloudFlare and the other in your phpBB website. So whenever you make a major change to your site you in fact have to clear the CloudFlare cache and the site's cache. Don't forget your browser cache as well.
To do this is very straight forward and simple. Prior to making any edits to your site, go into CloudFlare and put CloudFlare in Development mode. Now under the cache tab clear the cache. So long as your site is in Development mode, CloudFlare won't cache any content at the edge servers. Now make your site edits, and go to the ACP and clear your board's cache once done. Then go back into your CloudFlare dashboard and disable Development mode. Now everything will cache as normal.
Note that you should do this whenever you update your phpBB board. You might also want to temporally disable mod_security (if you have it) in cPanel.
I have written a tutorial at my website on how to properly use CloudFlare and gain all its benefits. Read my Sig on how to help protect your website from hackers, and in that topic is a link to my CloudFlare post.
In a nutshell, using CloudFlare is only half the battle.
Edit- You don't need to disable SSL. That is not a caching option and of course it's gonna mess with logging in since the cookies on your site should be set to secure. If you have enabled SSL/TLS on your site, leave the SSL option in CloudFlare alone.