Don't overthink this. Consciously trying to do one or the other is likely to lead to overtransitions (if you concentrate on turning your hips) or sluggish transitions with awkward shooting (if you concentrate on restricting your hips).
Do some transition work - dry fire and/or live fire - with targets spaced.* Apply time pressure and measure your performance (e.g., use a shot timer). Don't consciously think about the mechanics of moving the gun, just think about looking at spots on the target and having the sights show up shortly thereafter. The analogy that Ben Stoeger uses is that it's like using a mouse to move a pointer on the computer screen. You don't need to devote any conscious attention to which hand or arm muscles are going to activate to move the mouse... you just look at where you want the pointer to show up and do it.
If you have someone film you doing transitions, you will likely notice that if the targets are less than say 45° apart, you'll likely just turn your shoulders. As the targets get more widely spaced, your shoulders will turn more than your hips, but your hips will turn some. But this is not like a baseball or golf swing where you are intentionally creating tension in a kinetic chain by forcefully winding the hips ahead of the shoulders ahead of the hands. You don't need a lot of force to move the gun... and whatever acceleration you put into it has to be taken back out again as you get to the next target.
Other than overthinking it, the one other big error would be to substantially alter the geometry between your arms and your chest. It's not a great idea to keep your chest restricted and collapse one arm or the other to transition. Few people have that impulse, but if you do, fight that one. You do want your arm/chest relationship to stay broadly similar - changes in that really change how the gun recoils and even where shots tend to go.
*For example, set up two USPSA-type targets on 2 separate stands. Draw and shoot one target with two shots, then shoot the other with two shots. Begin with the targets 7-10 yards downrange and spaced 6 feet apart. Move the targets progressively further away from one another, while still keeping them about the same distance from you (this will quickly mean you need side-berms to shoot into).