Exim Listings on the CBL
Exim listings on the CBL are quite rare, and almost always mean that the machine itself is confused as to what its own name is.
You can either adjust Exim's configuration, or fix it so that the operating system knows the proper name.
Fixing the operating system is strongly preferred, see these instructions.
In the event that fixing the operating system is impractical, ensure that the Exim configuration variable primary_hostname is explicitly set to a fully-qualified name. (It should never be set to an unqualified name, but if it's not set at all, it will default to trying to guess the hostname from the system hostname and DNS.)