When adding a column to a column then the table header menu used to display/hide columns is not updated. As soon as a topmost column is moved to an other position the menu will be updated.

Reproducer:

import javafx.application.Application;
import javafx.scene.Scene;
import javafx.scene.control.Button;
import javafx.scene.control.TableColumn;
import javafx.scene.control.TableView;
import javafx.scene.layout.BorderPane;
import javafx.stage.Stage;

public class TableViewHeaderMenuBug extends Application {

private int colCount = 1;

private void init(BorderPane root) {
TableView table = new TableView<>();
table.setTableMenuButtonVisible(true);
root.setCenter(table);

// Top columns
TableColumn topCol1 = new TableColumn("Top Col 1");
TableColumn topCol2 = new TableColumn("Top Col 2");
table.getColumns().addAll(topCol1, topCol2);

// Subcolumns
TableColumn<?, ?> subCol11 = new TableColumn("Col 1.1");
TableColumn<?, ?> subCol12 = new TableColumn("Col 1.2");
topCol1.getColumns().addAll(subCol11, subCol12);

TableColumn<?, ?> subCol20 = new TableColumn("Col 2.0");
topCol2.getColumns().add(subCol20);

Button addColButton = new Button("Add Sub Column");
addColButton.onActionProperty().set(event -> {
TableColumn col = new TableColumn("Col 2." + colCount);
colCount++;
topCol2.getColumns().add(col);
});

root.setBottom(addColButton);
}

@Override
public void start(Stage primaryStage) {
try {
BorderPane root = new BorderPane();
init(root);
Scene scene = new Scene(root, 400, 400);
primaryStage.setScene(scene);
primaryStage.show();
} catch (Exception e) {
e.printStackTrace();
}
}

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

Start the reproducer. You will see a table with nested columns. Check the table header menu on the right side of the table header (+). It will contain 3 entries.
Press the "Add Sub Columns" button on the bottom of the window some times to add sub-columns to Top Col 2. Check the table header menu again. It still shows 3 entries.
Move Top Col 2 to column index 0. Now the table header menu will be updated.