That seems to be a design/implementation issue with PD.
By default, Shutterstock music clips are saved in the
Documents\CyberLink\PowerDirector\Shutterstock Cache Files\audio folder, but unless you added any of the clips you downloaded to a project, you won't see anything from that folder in your media library the next time you open PD.
It would be nice if they added a dedicated library like they do for the Background Music and Sound Clips that come standard with PD, and that's something you can request using Rate Us & Provide Suggestions under PD's File menu.
Two ways to access the existing downloaded Shutterstock content come to mind:
If you've just downloaded a whole bunch of clips and want to use them later, right-click on an empty sections of the Media Library and choose Export Library. When you want to access those clips again, right-click in the ML of your new project and choose Import Library.
Another way to access the downloaded content is to use Import Media Folder and then import the the entire download folder at the locaation shown above. The advantage to doing it this way over importing a saved library is that
all downloaded content will be brought into the library, whereas an exported library will
only have the content that was present when you saved it and no newer downloads will appear.