A tier is considered "managed" when it has been instrumented with the Agent Installer. In the Monitoring Settings tab, managed tiers are those that you can enable or disable in the Controller UI.

You may see tiers listed on the Monitoring Settings page that you cannot change in the UI. A tier is considered "unmanaged" when it cannot be instrumented by the Agent Installer. Unmanaged tiers include tiers that have been instrumented manually with the Java Agent or managed outside of Splunk AppDynamics. To monitor the unmanaged tiers, you must remove your previous configuration and restart the processes.