Well, clearly Lucas envisioned Tatooine as under the empire when he made the SE.

As for your interpretation that the empire wasn't in authority over Tatooine in ANH, I think the screenplay and novelization suggest that's a mistaken interpretation. They both have talk of the empire potentially taking over the Lars farm. That wouldn't be a risk if Tatooine was securely under the Hutts and not under the empire. Clearly the empire are in control here. They just are not very interested in Tatooine, hence the lack of a heavier presence. If Tatooine was really under the authority of somebody independent of the empire, the imperials would not be able to act like they're in authority there. The local authorities would object. Clearly the local authorities have to bow to the empire because the empire rules this area. Tatooine is merely on the edge of the empire's area of power, hence a far weaker presence.

If the empire didn't own the place they wouldn't be at risk of taking over Owen Lars's farm. Just because they didn't have troops based there doesn't mean they didn't claim the place. Tatooine is just so far out and minor that the empire doesn't bother with a regular presence.

And Tatooine being under the Hutts is not at odds with it being under the empire. Alderaan clearly had its own government too, but it was part of the empire. Plus I don't think Tatooine was intended to be under Hutt government when the OOT was made.