Run the code:

import javafx.application.Application;
import javafx.event.Event;
import javafx.event.EventHandler;
import javafx.scene.Scene;
import javafx.scene.control.Button;
import javafx.scene.layout.VBox;
import javafx.stage.Stage;

public class JavaApplication4 extends Application {

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

    @Override
    public void start(final Stage stage) {
        Button b = new Button("Change coordinates");
                
        b.setOnAction(new EventHandler(){

            @Override
            public void handle(Event t) {
                Stage newStage = new Stage();
                newStage.setWidth(100);//**
                newStage.setHeight(100);//**
                newStage.setX(stage.getX() + 50);
                newStage.setY(stage.getY() + 50);
                start(newStage);
            }
        });
        
        VBox vb= new VBox();
        vb.getChildren().add(b);
        Scene scene = new Scene(vb);
        stage.setScene(scene);
        stage.show();
    }
}

Run the code, click button and look at how new stages appear at the same position. Remove lines marked with //**, and code will continue working as expexted.