Spatial awareness can be defined as understanding the relationships between objects, and the rates of change associated with those two objects, which leads to the ability to realise if they will conflict or not.
So yeah its pretty much essential for ATC. And as regards cubes, you have to work out whether two faces of a net cube will become next to each other when the cube is constructed, so an amount of spatial awareness is required to be able to correctly identify the pattern.
Thus while they have sod all to do with ATC, they do have a bit to do with spatial awareness testing and this is probably the reason the testing company use them to discern who should and who should not go to stage 2.
Hope that answers your burning question zooker... If not I suggest you write a long letter to the testing company themselves