Where did you downloaded Tunnelblick from? If it is not from the official Tunnelblick website, that could be the problem.
Or it could be that the update that isn't signed is an update for a configuration (not an update to the Tunnelblick application itself). You'll have to talk to the people who gave you the updatable configuration. (Tunnelblick does not come with any configurations because we don't provide any VPN service -- we only provide software.)
Recent versions of Tunnelblick require that all update appcasts (for both the Tunnelblick program itself and any updatable configurations) must be signed with a DSA signature. The signature is an HTML comment that is prefixed to the appcast itself. It is one line of ASCII characters ending in a LF character, and looks like the following:
<!-- Tunnelblick DSA Signature v1 MCwCFDE1PY6ORux2Gq4SS9KuII/JrZwEAhR7xC1u3f1dfI5r2VJ4gNCkXT1sHQ== -->\n
(of course, the signature itself would vary with the appcast).