I've been getting little messages from the Hatch Kiosk saying someone hatched with a pet I had in there, and I was awarded a Hatch Pepper. But there are no Hatch Peppers among my reagents in my backpack. Do you only receive them when you withdraw the pet from the Kiosk?
I've seen a few people accidentally looking at their Pet Snack window instead of Reagents. Could it be that this happened? Regardless, you'll find your peppers listed in three places. 1) at the kiosk itself, 2) when you check Dr. Purreu's recipes, 3) in your reagent inventory. It will be added immediately after hatching.