Hi felix,
I don’t have any experience with using bedskirts on a split adjustable bed (we have a bedskirt but it’s on a queen adjustable) but I would guess that operating two twin XL adjustables independently could cause them to creep up yes. I don’t know if all of them cover the whole foundation but most of them that I’ve seen do.
Post #10 here has more information about mattress pads for those who want to add some extra softness to their mattress. Post #89 here has more about the pros and cons of different types of mattress protectors for those who just want to protect their mattress but affect the feel and performance as little as possible.
While it’s not my area of specialty … post #7 here and the posts it links to has more information about different types of sheets and bedding that may also be helpful.
Phoenix