Thanks, Helen. 'Calculate completion data' is set to run ASAP (* in all fields). I'm pretty sure cron.php is running every minute, but we don't host our own Moodle, it's on a hosted platform, so I've asked them to confirm that timing. Do you know whether the setting 'Completion mark as started' should run at the same frequency?
Looking at the default settings, it seems that 'Completion mark as started' doesn't need to be run every minute.