Constructs can exist independently. A construct is formed by the intent of the soul, but that conceptual pattern can continue to exist after formation. The first reason I am confident constructs are independent is the duration that they can last. A properly formed and sealed construct can last unchanged for at least many years, and probably longer. Even if it is a minor or irrelevant construct that one does not think about at all for this time. It seems much less reasonable to postulate that the soul remains undistracted and dedicated to actively maintaining trivial constructs for such a long time.
The second reason I am confident constructs are independent is the number of them that can persist. With practice making constructs you get a pretty good sense for how much conceptual complexity you can actively form, influence, or shape with your soul at a particular time. But you can make so many constructs that the total complexity of them can be more than thousands of times more complex than one's maximum manageable complexity. When they keep working greatly in excess of one's personal capacity, the most reasonable conclusion is that they do so independently.
And this property of independent persistence turns out to be a very important aspect of constructs, because it makes constructs as flexible and empowering as technology is for the material aspects of existence. I think we have only just begun to see what sorts of things are possible with this.