As mentioned in other forum posts Alfred relies on Spotlight when providing file search results. In MacOS the indexing of networks or attached drives is disabled by default. For those not afraid of the terminal you can manually turn on indexing this way:
mdutil /Volumes/DRIVE_NAME -i on
Once the mounted drive has been added to spotlight the search will show up.
If for whatever reason you want to turn off the search results you can use:
mdutil /Volumes/DRIVE_NAME -i off
Hope that helps!