You should be testing (ammonia, nitrite, and nitrate, also phosphate) as the rock is curing; because, it can begin to cycle while in the curing stage. The dead organisms on and within the rock kick off the nitrogen process, which encourages beneficial bacterial growth (cycling). You should see an expected order of organics: ammonia, nitrites and then nitrates, each of these represent a different form of bacteria now processing an organic compound in the water. Once this happens you can add the rock to your tank, and start slowly with live stock. Remember it takes time for the bacteria to grow and compensate for the higher organic loads of our tank additions.
I almost missed my ammonia spike, which would have made me wonder if it ever occurred and question if I had cycled my rock. Thus, why most people will recommend testing during the curing process. Also, Pukani by it's nature is very porous and you will hear people describe it as leaking phosphate. I don't necessarily subscribe to the rocks leach xyz, organic, but I do believe Pukani retains a tremendous amount of dead biological media and this leaches phosphate. This is more of the curing process, by curing the rock outside the display tank it is ultimately easier to manage unwanted organics with water changes or media before putting them into the display tank. IMO, it is much easier to reduce phosphate while curing, verses when it reappears in the form of nuisance algae in your aquarium later. I hope this helps and doesn't sound condescending. I too found cycling and curing confusing. I believe this came about because of the use of dry rock, which requires curing, verses the live rock we used to use, which required cycling.