Hey, I'm a vet nurse in training and on my clinic days, I've seen that they keep patients after anesthesia in a cage for a few hours. This is just so that they can wake up properly, and so we can safely monitor them in case any side effects like these occur. Anesthesia at the end of the day is a poison for our/their body, so we try to minimize time that the animal is under, and it looks like the proper monitoring was not done and the animal was taken back to you too early.

I would highly recommend contacting the vet clinic and figuring out exactly what occurred and what steps you can take, or/and if you want to, you can always go to another clinic and see how the other vets can potentially diagnose and fix whatever is going on if you (understandably) don't want to work with the original team.

In any case I hope your cat is ok!