The fractals are 3D textures. The background sphere is a 2D surface. The appearance of the background depends where the 2D surface intersects (slices through) the 3D texture. If you translate the 3D texture only, or you translate the 2D surface only, you change the appearance of the slice because it's a different part of the 3D texture.
Now, because this is a sphere that's centred on (0,0,0), you should be able to move the galaxy around simply by rotating the texture around the same point (0,0,0). This will work because all points on the sphere are the same distance from that point, so the slice through the texture is the same.
In Terragen you should be able to do this by adding a Transform Input shader at the very end of the shader network. Even if you have lots of other translations going on, if the rotation is the very last thing at the end of the network then it should work. But you can only use rotation, not translation. If you use translation in the very last transform, then you'll need to move the sphere by the same amount.
Matt