You are able to change the applicant's program/app cycle under the status tab, but when you revisit the application, the original program/app cycle still shows.
A possible solution:
Check to see if the applicant has any withdrawn applications for the desired program/app cycle.
If they do, the admin will not be able to switch the application to the desired program/app cycle.
The admin can choose to reinstate the old application and withdraw the current application or, they can scrub the withdrawn application and then switch the application over to the desired program/app cycle.