When clearing the alarm on a linked calendar record (i.e., a calendar record that has multiple users selected) the alarm is only cleared for that user. The alarm will still be displayed as specified for other users who have not yet cleared it. Likewise, snoozing an alarm only affects the user who snoozed the alarm.
However, keep in mind that if an alarm is linked to records for other users, entering a Date Completed will mark the record as complete and clear the alarm for all users. Likewise, clearing the Date Completed will mark the record as incomplete for all users.