The latest iMovie appears to hate NAS drives. It looks like Apple is now checking to make sure this is a true Apple file system (why???!). In any case, if you want to use a NAS or something else, you have to hack through this workaround:
1. Create a custom .dmg file that lives on your NAS. Then everytime you use iMovie, you have to mount this file (double click on it) and use that.
2. To get to it, in iMovie 10.0, you have to choose File/Open Library/Other and navigate to that DMG. Ugh. What a mess. It would be so nice if they just used regular directories. At least it is better than the even more bizarre scheme used in iMovie ’11 (love the version numbers!) which had a single library per hard drive.
Movie is asking for a disk that is correctly formated. You’re not able to format your NAS in the correct way so you need to create a disk image that is in the correct format. That image can be created on the NAS
disk utility – new image
Save as: your-name
Where: Network share
Format: Mac OS Extended (Journaled)
Partitions: Single partition – Apple partition map
Image Format: sparse disk image
via iMovie 10.0 and Network Drives | Apple Support Communities.