They travel through various sectioned off areas, until they arrive at a place that looks approximately like this. In various tubes and boxes they will find their confiscated belongings - or, at least, the stuff that was perceived of as 'noteworthy'. All normal clothing will be destroyed, leaving only items that are curiosities, magical, or otherwise unique. This mostly means that personal effects that aren't magical armor or something interesting are ostensibly gone.

There are also various animals, suspended in liquid-filled tubes. A large pink lion sticks out, as do a few different Pokemon, separated from the group during processing. Their Pokeballs are stored in a separate compartment nearby.

Your stuff is here, and Tyki can access it. Now, you just have to free those suspended here, and take the rest and leave.