There is nothing special that you need to do to your Delphix Engine to prepare for an upgrade, once you upgrade Oracle make sure that you refresh your Environments so that the Delphix Engine can see the new version. Then go to Manage>Databases> My Databases, open each dSource and/or VDB card and click the blue arrow to open the Database Upgrade panel; select the desired Installation and Environment User (if not showing hit Refresh) and click the check mark to finish. Please check out docs on
Upgrading a dSource and VDBs for full written instructions.