Those tutorials are oversimplifying. Lenses (and their relatives) transform operations, not values. Composition of lenses is exactly like composition of functions, with the inner-most operation on the right. A lens foo :: Lens O I transforms an operation on I into an operation on O. A composition outer.inner turns an operation on the target of inner into an operation on the source of outer.

This is demonstrated by the way over distributes with (.):

    over (outer . inner) = over outer . over inner

What confuses people is view, which is contravariant:

    view (outer . inner) = view inner . view outer

but you can’t avoid having one of over and view be contravariant.