To reproduce:
1. Run app.
2. Move mouse to one of the tabs and wait until tooltip pops up.
3. Press button "Set new tooltip".
4. Repeat step 2.
5. Nothing has changed.

import javafx.application.Application;
import javafx.event.ActionEvent;
import javafx.event.EventHandler;
import javafx.geometry.Side;
import javafx.scene.Scene;
import javafx.scene.control.Button;
import javafx.scene.control.Tab;
import javafx.scene.control.TabPane;
import javafx.scene.control.Tooltip;
import javafx.scene.layout.HBox;
import javafx.stage.Stage;

public class JavaApplication29 extends Application
{

    TabPane myPane;

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

    @Override
    public void start(Stage stage) throws Exception
    {
        HBox root = new HBox(10d);

        myPane = new TabPane();
        myPane.setTranslateX(200);
        myPane.setTranslateY(150);
        myPane.setPrefSize(200, 200);
        myPane.setSide(Side.TOP);

        for (int i = 0; i < 5; i++) {
            Tab tab = new Tab("Tab " + i);
            tab.setTooltip(new Tooltip("Tooltip #" + i));
            myPane.getTabs().add(tab);
        }

        root.getChildren().add(myPane);

        Button btnResetToolTip = new Button("Set new tooltip");
        btnResetToolTip.setOnAction(new EventHandler<ActionEvent>() {

            @Override
            public void handle(ActionEvent t)
            {
                for (int i = 0; i < myPane.getTabs().size(); i++) {
                    myPane.getTabs().get(i).setTooltip(new Tooltip("New Tooltip #" + i));
                    
                }
            }
        });
        
        root.getChildren().add(btnResetToolTip);
        
        Scene scene = new Scene(root, 600, 400);
        stage.setScene(scene);
        stage.show();
    }
}