Help integrating teams with program level: Can teams use sub tasks independent of stories?

[Ed Riefle]

We have several teams falling under a larger program. Our teams manage work in Jira and the Program uses Aha!.  Each time a new PM rolls on they change categories which affect the teams' workflow.  Most recently they have restricted the ability to move sub-tasks into testing and code review.  Is there a way to have separate categories at the sub-task level so that it does not disrupt the team workflow?