Hi, and welcome to the forum!
Every layer and group layer has its own origin, which is the center point from where the layer is transformed.
I'm guessing there are multiple origins involved in the setup, and you may be rotating on a different origin point from where the eye layer's origin is set. Fortunately, there are many ways to solve this (at least as many ways to mess this up.)
The most obvious one is to rotate only on the layer you want to rotate. So in this case, only rotate the eye layer and not its parent layer. If you want the parent layer to rotate the same way, you need to move the origin to match the child layer's origin. This gets tricky when you have a lot of child layers, though, or when you have rotated both the child and parent layers during animation, which can introduce animation conflicts because of the offsets. So, if you're going to rotate like this, pick one layer and stick with it.
Another is to bind the layer to a bone and rotate only the bone. This is the most common solution because most animators will try to keep most, if not all, of their animation keyframes in the bone layer. (Animation is easier this way.) The catch is that bones can rotate only on the Z axis, not X or Y. So, if you need X or Y rotation, we're back to rotating the layer.
If you want to rotate on all three axes, another option is to set up at least one Smart Bone Action to rotate the layer in any axis or all axes. This means using Smart Bones to rotate the layer and/or bone in the directions you want. Even better, you can animate this in the character's Bone layer along with almost everything else related to the character.
Without seeing your setup, I'm just guessing at the problem and solution you seek, but I hope this helps you sort it out.
