I think your problem is more likely how you mapped the texture on. I don't have a whole lot of experience with texturing in Maya, but in Blender I know there's different ways to determine the texture orientation, and some of those are based off of the world around it, not the object it is applied to. That would explain why the textures are only moving when the objects are moving; the texture technically is not moving at all. One way you could think about it is if you had a projector and a ball. The projector is projecting an image (your texture), and the projector never moves, but if you move a ball around in front of the projector (the ball being your object) the "texture" will change on the ball.
To solve the problem, you just need to figure out how to map the texture to the object its self, not simply project it onto the object.
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