You are correct. It would try to throw everything into space. The only thing is, it would be throwing it into what you're thinking of as the ceiling, but is their floor.

It would work the same way the water stays in a spinning bucket. The water tries to fly away, but the bucket holds it into place.

On the spinning Eros, the people try to fly away, but the stone keeps them in place.

https://www.youtube.com/watch?v=Zjqrx7wrpJc