At the beginning of the animation, did the water stay in the bucket or did it spill out?

It seems as if the water in the bucket is defying gravity, but is it really? No. Gravity-the force puling down on everything - is still at work even when the bucket and water are above your head. The water's inertia wants to keep the water traveling in a straight path, but gravity is acting on the water, causing it to fall in a downward path that will eventually hit the earth.

If you put a tennis ball under your open palm and push it down through the air hard enough, you can make it stay in contact with your palm. This happens because you're forcing it to accelerate down faster than it could fall.