It is not clearly stated in the Help but Solids are always exported with a standard orientation of Z pointing in the direction of the normals of the plane. This means that, if you create a plane object in the perspective view, it will be created with a default orientation of +Y. If you want it to be vertical you will probably rotate it 90 degrees in the Heading. But that will make the Z axis of the plane point upwards. Since Solids create planes that have the Z axis parallel to the normals of the plane, the created Solid will be a plane on the XZ plane with the normals pointing upward (the direction of the Z axis of your plane object). So, your plane object is now flat on the XY plane but the Solid will appear in AfterEffects in the XZ plane, hence, rotated.
Make sure the Z axis of your plane always points in the direction of the normals. This means that you need to create a plane and set its orientation to +Z or simply rotate its axis (needs to be a poligonal object, of course) so that the Z axis is perpendicular to the plane surface.