JavaFX (with FXML) MVC: Model use Controller

Models should not have any reference to the controller(s), or to the view(s). You should make the properties of the model observable, so that interested clients (the controller or view) can observe them and receive notification when they change.

The best way to change the UI periodically in JavaFX is to use the Animation API, e.g. a Timeline.

So you can do

private class FibonacciModel {

    private final IntegerProperty currentValue = new SimpleIntegerProperty(1);

    private int previous = 0 ;

    public IntegerProperty currentValueProperty() {
        return currentValue ;
    }

    public final int getCurrentValue() {
        return currentValueProperty().get();
    }

    public final void setCurrentValue(int value) {
        currentValueProperty().set(value);
    }

    public void nextValue() {
        int next = previous + getCurrentValue();
        previous = getCurrentValue();
        setCurrentValue(next);
    }
}

And then your view can do

public class FibonacciView extends VBox {

    private final Label label ;
    private final Button startButton  ;

    public FibonacciView(FibonacciModel model) {
        label = new Label();
        label.textProperty().bind(model.currentValueProperty().asString());

        FibonacciController controller = new FibonacciController(model);

        startButton = new Button("Start");
        startButton.setOnAction(e -> {
            startButton.setDisable(true);
            controller.animateNumbers(20)
                .setOnFinished(event -> startButton.setDisable(false));
        });

        getChildren().add(label, startButton);
    }
}

and

public class FibonacciController {

    private final FibonacciModel model ;

    public FibonacciController(FibonacciModel model) {
        this.model = model ;
    }

    public Animation animateNumbers(int howMany) {
        Timeline timeline = new Timeline(
            newKeyFrame(Duration.seconds(1), event -> model.nextValue());
        );
        timeline.setCycleCount(howMany);
        timeline.play();
        return timeline ;
    }
}

In you controller which implements Initializable, you'll have the @override method : initialize

In this you'll create your model :

model md = new model(); //depending of you constructor

To add you controller to the model you can give in throught the constructor :

//in initialize of controller
model md = new model(this); 

And

//in you ctrl.java
private ctrl control;
public model(ctrl control){
    this.control = control
}

With this you'll be able to do :

public int fib(int n){
    control.setLabelFib(n)
    Thread.sleep(1000);

    if (n <= 1) return n;
    else return fibonacci(n-1) + fibonacci(n-2);
}

I write the method to wait also

Try and tell in comment how it works