Each animation has an 'Empty' arrow above it, all parts of the animations including objects, forces and the particle animations themselves are parented to this empty. Use this to move, rotate and even scale the entire animation to your liking.

Not to worry! Sometimes Blenders particle system can freak out. To make them work as normal, simply change any value slightly under the particles settings such as 'Seed'. Go back to the start of the animation and hit the space bar, the animation should now be working as normal.