It's a combination of filming greenscreen for the carefully lit characters, then color grading them to high contrast with a lot of white so they can be multiplied over the artwork.
having an artist do the stylized artwork for the pastel color backgrounds
keying and rotoscoping in the people
animating and compositing a lot of subtle particle systems and perhaps inktank footage to do reveals of the layers. re-using some of the actual pastel scans, or rebuilding them with effect footage
multiplying over paper texture, having a soft turbulent displacement,
I'm pretty sure there's some handanimated art in there as well.