Nested tree does not correctly update

Bug, feature request, or proposal:

Bug

What is the expected behavior?

Adding a node to the tree and firing a change event should update the tree

What is the current behavior?

The tree does not update

What are the steps to reproduce?

StackBlitz link line 123

Open the example, and within 10 seconds expand the Applications node.

The following code should add a node, and the node should be displayed:

    database.dataChange.subscribe(data => {
      this.nestedDataSource.data = data;
      console.log(data);             // <-- see screenshot below
      });
    console.log('Please expand the Applications node within 10 seconds');
    setTimeout(() => {
      const data = this.nestedDataSource.data;
      for (let node of data) {
        if (node.filename == "Applications") {
          const newnode = new FileNode();
          newnode.filename = "ghost";
          newnode.type = "gs";
          node.children.push(newnode);
          console.log("Added component");
        }
      }
      // force change
      console.log("Forcing change");
      database.dataChange.next(data);         // <-- firing event here
    }, 10000);

After ten seconds the console correctly logs the added component:

But the view does not update:

What is the use-case or motivation for changing an existing behavior?

I would expect the tree to mirror the underlying data model.

Which versions of Angular, Material, OS, TypeScript, browsers are affected?

It happens on chrome, with the latest version of the library.

Is there anything else we should know?

Sorry I could not make the example autoexpand (please see #13027 on why)