the completion criteria that are packaged with core iterate through their completion criteria, and when a record is identified, they mark the requirement as complete, and pass a timestamp to indicate when it was completed. This can be seen here:

https://github.com/moodle/moodle/blob/master/completion/criteria/completion_criteria_course.php#L197

https://github.com/moodle/moodle/blob/master/completion/criteria/completion_criteria_activity.php#L239

https://github.com/moodle/moodle/blob/master/completion/criteria/completion_criteria_grade.php#L225

Currently, the completion_criteria_completion::mark_complete() function does not take a timestamp value. see: https://github.com/moodle/moodle/blob/master/completion/completion_criteria_completion.php#L106

Rather than remove the values being passed to mark_complete(), It should be that mark_complete can accept and use a timestamp. If this doesn't happen, the completion time is bound by the cron-run time rather than the actual time the action happened.

The attached patch corrects mark_complete() to accept a timestamp, and use it if it's available. If not, the system time() is used as before.