My guess is that the layers don't read across scenes?
The default layering mode does not read across scenes, rather it 'flattens' each scene to provide the cleanest possible scene transition.
There is another layering mode available, that does not flatten scenes, and provides the cross scene layering you were looking for. Note: You can change the layering mode for the entire project only. The setting is available Under File/Layering
@AlexWilliams - or to build on @jhoepffner's scene - make your background a blur of the source as well - is that what you meant? the 'blur gradient' is affected by the amount of blur on the shape, and the background blur is the maximum outside.