Stat does not interface or integrate with Peoplesoft Update Manager (PUM). You have to use PUM along with change assistant.
Please see attached document of how change assistant can be integrated with Stat. In fact, it's not a truly integration.
It's more like using stat workflow to document the applying patch process via change assistant.
You have to use change assistant to apply the patches via demo environment first.
Once the project is in demo, then you can read the project into stat and migrate across other environments.