i really want to believe they mean turning them inside out and hanging them by the waistband. the alternative would be too retarded, but they hang them in the first place, so who knows...
PSA for everyone else, NO do not hang your petticoats that are made of a soft material. i've seen it recommended more than once and it's outright wrong. store them in a drawer, or in a bag, or something to that effect. they will floof right back up after you take them out of the compressed space.
if it's the scratchier hard tulle material, then hang it. if it's soft, stuff it somewhere.