Thanks for reporting!
Let me explain the mechanics of pet spawning in details. We apologize that it wasn't described fully yet. Your question shown us that it can be unclear for the users.
When user catches a pet, the new pet gets a counter up to 8 cycles (32 hours) when it will be spawned. After the counter gets to zero, a random pet species rolls depending on what dens are free. If user has a free ground den, there's always a chance that the new pet will be of a ground type and go there. This is what has happened with you. This new pet isn't bound to the den where it predecessor was caught. So the best recipe to get the flying dens inhabited as soon as possible is not to catch the ground pets.
Concerning the abundance of Pumas, it's a coincidence which happens from time to time. I remember the other user had the same issue with Cockatrices for several days.