I just tried reaching your site and thejukeboxrebel.wikidot.com is the only address that works. www.thejukeboxrebel.com displays a DNS error.
In order for the custom domain to work, you have to configure your CNAME record using your domain registrar's control panel. For example, I use 1and1.com to register my domains and for sites hosted on Wikidot, I simply edit my domain's DNS setting and set the "A/AAAA and CNAME Records" to either 220.127.116.11 or 18.104.22.168 as explained by Wikidot in the Custom domain setting in our _admin panel.
Once that's done, I edit the custom domain setting in my Wikidot control panel and set my Custom doamin to www.mydomain.com and also set up a 301 redirect to mydomain.com (without the www prefix). That way, if someone types the domain name without the www, it redirects automatically. In case it's not clear, substitute "mydomain.com" with the domain name you registered.
I usually don't check the "Use the custom domain as the only domain for this site." until I verify everything is working. BTW, if you ever get stuck after checking that box, you can always access your control panel via your original Wikidot site URL (i.e. mydomain.wikidot.com/_admin) so you can uncheck the box until you figure out what's going on.
If everything is working correctly, the only URL that won't redirect to your custom domain is the _admin page.