How to build an egg timer in Drupal
You have two approaches.

You could create a non cacheable block, that will check a session_variable, if a timer is set and the time is passed. If is has, it will render something, else it will be invisible. The will create the pop up on page refresh.

Alternative you can use a javascript and use setInterval to check if the time has passed and then display a popup. You would then have to add the javascript info on page load.