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When I add a Single Bone and then an Empty object to the scene, as follows:
single bone and an empty

Then I add a Copy Rotation bone-constraint, I set the Empty object as the target, the constraint will rotate my bone on the X axis by 90 degrees:

copy rotation constraint rotating bone

Although neither the Armature, nor the Bone and not even the Empty has any rotations whatsoever.

My question is: why is this happening and if this is the expected behavior, then how can I prevent it from happening?

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First, yes it is supposed to happen. If it is expected or not depends on whether on not you have read this answer. :)

The reason this happens is because bones in blender are not Z up like everything else, but the Y axis is up.

Here is a picture set up the same as yours, but with the axis display turned on for the armature.
bone showing the Y axis is up

You can easily "fix" the offset by changing the rotational space from World to Local with Parent. (You will in most cases want to use local with Parent space anyway.) Copy rotation constraint settings


Try rotating the bone in edit mode, then see what the constraint does with Offset turned on and the Space set to World. (Hint, you will end up needing Local with Parent.)

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I still have no idea why, but it looks like, that turning the Offset option to True (place a tick into the option-box) will solve the problem:

enter image description here

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