Two possibilities. First, as @Jonty noted, make sure you have your “clean up inbox items which have:” set to A Project. Second, if you already have that configured that way, then what you may be having trouble with is the timing of the clean up. The preference there is called “Clean up items completed.” You can choose “Immediately,” or “When changing perspectives.” I like to keep mine set to “when changing perspectives.”
If you have yours set up the same way, you can force the clean up when you want. There is a tool you can put on the tool bar that looks like a brush. When you press it, the perspective you are looking at (whether inbox or something else) will clean up.
These preferences are the same on iOS, even though my screenshots are from the Mac.