Most hosters do not allow you to open port 53 (DNS) in any way if you are a private customer and not a company.
So even with running DNS in CWP the CWP Zones aren't taken.
To make the DNS Zones working you really need to have port 53 open, and thats what most ISP deny for security reasons, and you need to set your CWP Nameservers on your Hoster/Registrar to work properly.
So also on mine, CWP DNS Zones are just here for info and i need to add SPF, DomainKey etc to my real hoster to work, as i don't have 53 open to the world.
Just don't care about the CWP local DNS zones or deactivate it like igor told you.