Chat history can be stored on the server, on individual clients, or not at all. Trillian also gives users control over chat history storage at the individual service level, so users can log Trillian-to-Trillian traffic but not log Jabber/XMPP traffic, for example. You can either allow your users the right to configure these options individually or you can choose to enforce these options in a way that will prevent the client from modifying them.
Trilian for iOS, Android, and Web do not store chat history on disk regardless of how your policy is configured.
Configuring chat history storage
From Policies, double click the policy you wish to change.