There should be no reason to use a pressure dressing underneath the eyes after lower eyelid surgery. Perhaps your surgeon just meant cold compresses, not compressive dressings per se.
If bleeding should occur, it might be trapped in a tight space, or go unrecognized. This could lead to very damaging pressure on the eyeball and optic nerve.
Usually doctors recommend ice, elevation, decreased activity postoperatively. Surgery should be carefully performed, to minimize bleeding. The patient should be medically optimized before surgery, to reduce the chance for high blood pressure (a leading cause of bleeding). The surgery should be performed in a monitored setting in an accredited surgical facility, to see if potentially dangerous early warning signs of changes to the vital signs are there.