It looks to me that most of the bulk is up/down and not side to side. I'd guess the white jellyroll was cut a slight bit wider than the pinks.
I've had some really bad "pillowing" on a quilt my Mother had made 30 years ago. I think it's why she never quilted it. I couldn't do an allover pattern, but by using motifs, I was able to ease the excess and it turned out fine. It still looked quite "poofy" in the center compared to the outer edges, but it did lay flat and looked nice.