When you export a QuickTime movie from Final Cut Pro and then import it into Final Cut Pro, the Alpha Type of the resulting movie is set to Straight by default when you export by choosing File > Export > Using QuickTime Conversion, and export to Prores 4444 with an Alpha Channel (Million Colors +).

Programs
Final Cut Pro 7.0

Solution

Set the Alpha Type setting to Black, this is the correct setting to use for Prores 4444 clips with an Alpha Channel.
Note: To check the Alpha Type of a clip in Final Cut Pro, select the clip in the Browser, then choose Modify > Alpha Type.