in the supine hip extension with a swisball on the feet. Palms should be facing up because??

Generally palms up because you can then stabilize the scapula with retraction and depression. The Scapula musculature is the back top side of your core stabilizers. You will probably find your clients shrugging and rounding their shoulders while lying on the floor.

You can also place the hands at different position at your side. Generally the wider the hands the easier the exercise. So keeping your arms closer to your side will be less stable. So again depending on your goal and each client may be different.