Matt,
The problem is that Time & Expense users do not have direct access to Tasks in Clarizen unless they are To Do work items created by the user. T&E users are specific to adding time and expenses within Clarizen and update Tasks on the Work plan via Progress Update Reports.
If you want your users to have Task Management access, you will need to give them Team Member licenses. This will still not allow access to the Project level (this requires Full user license) but will give them access to Tasks and should resolve your issue.