Hi, I'm not a Quantum user, but my guess would be that the standard Quantum reflector will not fit inside the Speedring/Lollipop of the Ezybox Hotshoe. So Lastolite came up with a safe way of getting the flash-head inside the box.
However that applies to the original Lastolite Ezybox Hotshoe - which had a pretty narrow 'throat'. Lastolite has move on and now has versions of its pop-up (& other) style Softboxes with very much larger apertures, so if I was a Quantum user, I'd check out their latest offerings on their home site. Cheers