CountdownController.cs

using System.Collections;
using UnityEngine;
using UnityEngine.Events;
using UnityEngine.UI;

public class CountdownController : MonoBehaviour
{
    public int seconds = 10;

    public Text countdown;

    [SerializeField]
    public TimerRunoutEvent timerRunoutEvent;

    void Start()
    {
        if (countdown == null)
        {
            countdown = GetComponent<Text>();
        }

        // TODO: REMOVE IN PRODUCTION! :) This is for debug only
        StartCountdown();
    }

    public void StopCountdown()
    {
        StopAllCoroutines();
    }

    public void StartCountdown()
    {
        StartCoroutine(DoCountdown());
    }

    IEnumerator DoCountdown()
    {
        for (int i = seconds; i >= 0; i--)
        {
            yield return new WaitForSeconds(1);
            countdown.text = i.ToString();
        }

        timerRunoutEvent.Invoke();
    }
}

[System.Serializable]
public class TimerRunoutEvent : UnityEvent
{

}

QuitOrContinueController.cs

using UnityEngine;
using UnityEngine.EventSystems;
using UnityEngine.UI;

public class QuitOrContinueController : MonoBehaviour
{
    public CountdownController countDownController;

    public Button defaultButton;

    void Start()
    {
        EventSystem.current.SetSelectedGameObject(defaultButton.gameObject);
    }

    public void ContinueGame()
    {
        countDownController.StopCountdown();
        // TODO: Continue
        print("Continue the game!");
    }

    public void QuitGame()
    {
        countDownController.StopCountdown();
        // TODO: Quit
        print("QUIT!");
    }
}