Selecting the first entry and pressing the button raises the issue that the focus moves downwards while the selection is still correct.

public class GuiTestMainFocus extends Application {

    @Override
    public void start(Stage primaryStage) {
        Button btn = new Button();

        final TreeItem<String> treeItem = new TreeItem("Items");
        List<String> stringList = new ArrayList<String>();
        for (Integer i = 0; i < 10; i++) {
            stringList.add("Test " + i);
        }

        TreeView<String> treeView = new TreeView(treeItem);

        btn.setText("Set new list and select oldIdx!");
        btn.setOnAction(new EventHandler<ActionEvent>() {
            @Override
            public void handle(ActionEvent event) {
                List<String> stringList = new ArrayList<String>();
                for (Integer i = 0; i < 10; i++) {
                    stringList.add("Changed " + i);
                }

                Integer oldIdx = treeView.getSelectionModel().getSelectedIndex();

                List<TreeItem<String>> treeItems = new ArrayList<>();
                stringList.forEach( p -> treeItems.add(new TreeItem(p)));

                treeView.getRoot().getChildren().setAll(treeItems);
                treeView.getSelectionModel().select(oldIdx);
                treeView.requestFocus();
            }
        });

        stringList.forEach(string -> treeItem.getChildren().add(new TreeItem(string)));
        HBox root = new HBox();
        treeView.setShowRoot(false);
        root.getChildren().addAll(treeView, btn);

        Scene scene = new Scene(root, 300, 250);

        primaryStage.setScene(scene);
        primaryStage.show();
    }

    public static void main(String[] args) {
        launch(args);
    }
}