Yes - the standalone web app contains an embedded rather than a shared engine. Hence if you package up your own process in a war file and deploy to tomcat, I don’t believe the embedded engine will be aware of your app (note Im a little unfamiliar with the embedded engine architecture). I assume you would have to add you process to the app and rebuild, and deploy it for your process to be included.
Hence my recommendation would be to download and install the pre-packaged full distribution. Thus if you deploy your war file, it will run in the context of a shared engine.