This is due to a setting of the Live Schedule Post online and on export settings when printing schedules. To fix this, go to the Web Terminal pane inside of MSP and click on the Full Schedule tab. From here, click on the name of the schedule in the Live Schedule Posts box, then click the small "Settings" button just to the right of the list of schedules.
This will open the "Online layout settings" screen and on that first screen, un-check the option that says "Alphabetize volunteers in (unnumbered) ministries by last name" and then click Save. This will make the Web Terminal schedule report volunteers in the same order they appear inside of MSP.