The reason the student's school years are out of order is because their Student Enrollments are out of order.

In order to check this, follow these steps:
  1. In Core from the  Users/Access dropdown, select Profile
  2. Stay on the Edit User Profile Data tab and search for the student
  3. Scroll down to System Information and click on Student Enrollments
  4. Make sure that all the dates for each year are correct
Once the dates are correct, if you view the transcript again, the school years should appear in the correct order.