Hi Zach,
I'm not sure this is possible. You can trigger a subscription of the creation or deletion of a relationship but in the case of a creation, the workflow engine will not differentiate between a 'new' relationship' (first assign) and a 'replacement' relationship
(re-assign).
Also, the Cireson App is designed to notify the Assigned User (Analyst), not the Affected User.
I think you would need a custom workflow, that can check the history of the WorkItem or look for deleted relationships for that WorkItem to see if it is a first assignment or a reassignment.
Geoff