i wouldn't say fat redistribution, no. think back to your biochemistry. The gluconeogenic pathway is protein-> amino acids-> carbon skeletons/citric acid cycle intermediates/pyruvate-> malate-> glucose. Fat, by contrast, doesn't break down to glucose precursors, it breaks down to acetyl-CoA. You can use acetyl-CoA to make ketones, but not glucose; for that you need the citric acid cycle intermediates.
Cortisol doesn't have any lipolysis activity. If you have Cushing's, you have too much cortisol, which means you are breaking down protein (mostly muscles, and mostly in the periphery) and liver is making that protein into glucose that your body doesn't really need. Then the excess glucose gets made into fat in adipose cells because insulin is being secreted in response to hyperglycemia. So you have peripheral muscle being made into trunchal fat, hence the classic Cushingoid appearance with thin limbs and central obesity.