First, I think it's useful to clarify exactly what the surgeon is doing here:
The Five-Step Lower Blepharoplasty: Blending the Eyelid-Cheek Junction.
Rohrich et al. Plastic and Reconstructive Surgery. 2011.
In addition to aesthetic benefits, the functional and supportive role of cheek fat on lower lid shape has been elucidated by numerous surgeons. Whether cheek-lower lid soft tissue is augmented through fat mobilization, direct injection, or by means of implants, the goal remains the same.
What we're seeing at the ~12 minute mark is fat processing and mobilization. Why is the surgeon doing this? Because, as the tissue has been severed from its original blood supply, "fat grafts must obtain oxygen via diffusion until neovascularization occurs:"
Diffusion and Perfusion: The Keys to Fat Grafting.
Khouri et al. PRS Global Open. 2014.
Therefore, it seems that the core principle of fat graft survival is that oxygen concentration at any point in a graft is a function of the oxygen concentration of the surrounding capillaries, the diffusion rate of oxygen to reach that point in the tissue, the distance from the oxygen source, and the metabolic rate. In other words, at every point within a fat graft, there is a race between the rate at which oxygen is needed by the cells and the rate at which oxygen can be delivered by the capillaries and diffused through the adipose tissue.
Although this review largely centers on fat grafting via injection, the relationship between oxygen diffusion limits and tissue thickness (graft radius) holds true regardless of the exact surgical method of fat harvesting, processing, and reinjection. In my comment, I summarized this as "reducing the perfusion requirements of the tissue," which is technically true, but it should be noted that the grafted fat is initially dependent on diffusion (circumventing "perfusion requirements") before eventual revascularization.