If somebody plays the "Pandamonium" card on my stable, and then on their next turn they play a unicorn card in their stable that can destroy unicorns at the beginning of their next turn. Would that mean they can destroy the formerly unicorn cards in my stable even though they’re technically pandas?
You don't have any unicorns in your stable
Pandemonium turns all of your unicorns into pandas for all other effects. This means that any effect that does something to the unicorns in your stable will see that you have zero unicorns and act accordingly.
This can be a pretty powerful protective shield at times. The catch is that you can't win the game while it's there.