What it does is manipulates the mycocelial mat that’s symbiotically fused with it’s skin. The mat will be partway through the process of infesting (and digesting) the rotting flesh of the prey, converting it to more fungal mass that the corpse back will slowly consume (like fat).
This has advantages for the corpse back and the symbiotic fungus. The corpse back gets added protection, a way to get extra nutrients from its prey, a slow-release external digestion method and even (with some simple electrochemical stimuli) extra limbs. The fungus gets hugely increased mobility and access to a high-oxygen-high-sugar energy source for when it’s needed (this also allows the mat far greater function than you’d usually see in your average fungus). Win win.
This gives the appearance of moving the flesh around because the mycocelial mat will (as a matter of course) grow into the shape of the victim, and any undigested skin, bones or bits of flesh will be held in that shape by the fungal mass. The tendrils are the fast-growing sugar fueled precursors to the main fungal infestation, which then takes its time growing into a near perfect replica of the deceased. This also has the advantage of being species agnostic. It doesn’t matter exactly what the corpseback has killed and subsumed: the mycocelial mat doesn’t care as long as it’s not fighting back any more.
Over time the figure of the prey will become more and more formless as damage occurs, the mass gets reabsorbed for calories/nutrients, bones and teeth get expelled, fungal fruiting bodies sprout etc. but for a while at least the Corpseback will have its very own mushroom powered, partially decayed puppet.