The name matches a surgery, so confirming the method matters.
When under-eye fat pushes forward and the area below it is hollow, a shadow forms at the border. This approach eases that border by placing an injectable through a blunt-tipped cannula. The name also refers to surgery that moves fat through a small incision inside the eyelid, which is a different procedure. It is worth confirming what is being placed and in which layer.
Under-eye injection softens the border between the under-eye bulge and the hollow beneath it. When fat protrudes and the area beneath sinks, a shadow falls between the two planes, and this fills that border so the surfaces run into each other. Unlike the surgery of the same name, it uses a blunt-tipped cannula.