I'm a stickler for keeping my gear off the ground -- hammock and tarp -- so I prefer set-ups that allow me to pack up quickly and without ground interference.
It helps to have a double-sided stuff sack, Bishop bag, or even skins to make packing easier, although it is possible with a regular stuff sack.
With a double-sided sack or bishop bag your sack should still be attached to the end of the tarp where the Dutch hook is connected (or one mini carabiner, depending on which version you're referring to).
Unhook the side opposite the stuff sack -- this would be the DutchWare Stingerz/Tarp Flyz end -- and begin stuffing into the stuff sack.
By leaving this one side attached, you can pull against this "anchor" as you stuff, which keeps the anchored side off the ground (like having a second pair of hands).
I'll see about creating a follow-up video to show how this is done. Stay tuned.