When I took another close look at the photos, I realized that the fullness is in the top and bottom rather than the sides. There are quite a few different mistakes that can cause this problem.
It looks to me as if he did not accurately square the quilt on the frame before starting, as the panto going from left to right is lower on one side than the other. This means the top of the quilt was not completely parallel to the takeup roller when he started. The problem probably started right there, with the loading of the top. Also, he may not have basted the quilt top to the batting and backing before starting the panto. This would account for the uneven fullness at the top of the quilt, as the top edge would not have been secured when he started.
It looks as if there are areas of fullness between the pantos also. This is probably caused by not using side tensioners, and also by not being careful about how the top is rolled and unrolled. Most people do pantos from the back of the machine, so he probably could not see the fullness developing as he quilted (being focused on moving the machine).
Basting the top and sides before starting should help, as would side tensioners. Before doing the last panto, he should probably also baste the bottom edge of the top (to the batting and backing) so it doesn't move around. The fish are really cute, but it is also their largeness and the large unquilted areas between them that tend to create this problem. A close quilting pattern will likely not allow such large areas of the top to become distorted during the process.
Being careful to keep the top perfectly aligned with the rollers and with the sides of the frame would help, as does basting as you go.
There are lots of Youtube videos that are helpful for beginning longarmers.