Of course the script isn't running each second, GM-scripts run once when the document has been loaded.
Calculate the difference between the current time and the target-time and use a timeout based on the difference:
var now=new Date(),
then=new Date(),
diff;
then.setHours(16);
then.setMinutes(15);
then.setSeconds(30);
diff=then.getTime()-now.getTime();
//when time already has been reached
if(diff<=0){
window.alert('you\'re late');
}
//start a timer
else{
window.setTimeout(function(){window.alert('it\'s time');},diff);
}