By default, faces in Named Selections are not selected to be inflation boundaries when the Use Automatic Inflation control is set to Program Controlled. However, you can select specific Named Selections to be included in Program Controlled inflation. To do so:
Click the desired Named Selection in the tree and then in the Details view, set the Program Controlled Inflation option to Include.
In the mesh controls, set the Use Automatic Inflation control to Program Controlled. As a result, the Named Selection you chose in step 2 is selected to be an inflation boundary, along with any other faces that would have been selected by default.