If you press ⌘-⌘ (or whatever keyboard shortcut you have configured for Manuscripts) to open up Magic Citations from Papers3b and it opens up a whole new copy of my Manuscripts document, make sure that you have only one copy of Manuscripts installed.

The issue is caused by Papers not being sure which copy of Manuscripts it should send the citation commands to (a limitation inherent with the AppleScript based communications it makes with Manuscripts).