Use php time(); function. Then when they do anything within your php script, you can get the time they did it without using a submit button.
Even if the script is just a display one, it will work.
$now = time();
$now is your integer, I prefer to let php handle the dates and times in this format instead of using mysql's timestamps or date formats because it's WAY easier from my experience. You can call up the date, time, hour, minute, second, year etc by using:
$when_they_did_it = date("l m/d/y h:I:s", $date);
Works wonderfully.