I am very sorry to hear of this very tragic accident that led to your Tiggy's passing...
You have my deepest sympathies.
I can imagine what you must be feeling and please try to not be too hard on yourself. Even though you trusted your Tiggy to stay on the top level of your house and going downstairs was not something your budgie girl would do, at the end of the day, our pets can have moments where they act erratically and will do something unexpected, and we must take this factor into account.
This is exactly why they shouldn't have free reign of the house when there is no person there to closely supervise, and especially so when there are cats or other larger pets in the household.
Again I am deeply sorry for your loss and that you had to learn this lesson the hard way.
I truly hope you are able to free yourself of the guilt and with time manage to heal from your loss.
Rest in peace beautiful Tiggy. You were much loved and will be missed.