After connecting the volume:
Choose Edit > Import file maps from the local menu of the Project Manager.
Why does this work?
When scanning a volume with the project manager, a filemap is created in the root directory of the scanned volume. The data is stored as a hidden file named ".Logic PM Database" in Mac OS X (this is also the case with internal volumes). The function Edit > Import file maps from the local menu of the Project Manager reads this file and provides the Project Manager data for the volume immediately.