This is an old project by Studio Moniker (Amsterdam)… I was once at a presentation of their work at Resonate in Belgrade (memories…) and they explained that the slight delay before the reveal of the underlying image is added artificially to add a bit of drama.
Btw, the correct image is loaded through a Voronoi diagram.
Conspiracy theory: that explanation is a lie, and the real reason for the delay is that it helps hide the fact that there isn't a unique image mapped to each pixel. If you click two pixels very close together, it shows the same image, but slightly shifted to exactly match your pointer. If the images were displayed immediately, it would be much more obvious what's going on.
Btw, the correct image is loaded through a Voronoi diagram.