Yes, the fleece "pillow case" stays put. I have hardly used the blow-up Sea-to-Summit bag. I just tried it out to assure myself it wasn't as noisy as the more expensive "premium" blow-ups. And again, I mostly kayak camp, so weight and bulk, though a consideration, are not as crucial as when backpacking.
But more influentially, I hardly ever need a pillow at all. The hammock supports my head just fine, so the pillow is mostly used as a support under a knee or next to my head to push the bugnet away. It's more of a "change of pace" item - something to switch things up a bit. I usually wear a sleep beanie. I don't like nylon against my skin. I sleep in light ankle socks, PJs, and a light beanie or balaclava in the winter. It's easier to wash clothes than to wash down filled gear or a hammock. And changing into some soft cotton after a day on the water or trail signals my body that it's sleepy time.
Note that "hardly ever ..." Sometimes, in the wee morning hours - not when I initially go to sleep - I might wake a little and my body is just a pile of relaxed bones and skin. At those times, I can fetal up on my side and put the small pillow under my head to keep a comfortable neck alignment.