There are two ways to think about your shot: cognitively and experientially.
When you think cognitively, you think in words: you analyze things, plan things, and form judgements about things. Cognitive thinking occurs in the past, the future, or in some abstract place out of time, but not in the present.
When you think experientially, you don't think in words. You are aware of your surroundings and what your body is doing. You use all of your senses to experience existence. Experiential thinking is non-critical and occurs only in the present.
When you are learning to do something, you first have to learn it in words: cognitively. You are awkward at first because you are constantly bouncing back and forth from an abstract thought about something to trying to perform that thought in the present.
After you have learned the movements, you begin to think experientially, rather than in words, which allows you to carry out both your thoughts and actions in the present. This works well until you notice that the arrows are not going where you want them to, or they are going all over the place. Then you have to switch back to cognitive thinking to figure out why this is happening, and you form a hypothesis. You test this hypothesis by first letting your cognitive mind guide your actions, since they are new and your body hasn't learned how to do them yet. If the hypothesis seems to be working out, you then practice the new movement enough times that your experiential mind can take over. You can't expect to shoot very well while you're going through this problem solving process, because you're trying to switch your mind in and out of the present. This is one reason why many people prefer to solve these problems in front of a blank bale.
If you try to shoot while still cognitively thinking about the problem, of course your shooting will only get worse, because you're trying to shoot while your mind is in the future, the past, or some abstract place out of time, and you can only accurately shoot arrows in the present.
Whether you prefer to focus on the target and run the shot in the background, or vice versa, you should be thinking experientially rather than cognitively, unless there is some particular problem you are trying to solve. In other words, in a normal shot where you are just trying to do everything the same as you already know how, you should be thinking experientially, by being aware of what you are doing, without words. Cognitive thinking should be used before the shot, to plan it, and after the shot, to critique it, but not during the shot, unless you are learning something new that you don't know how to do experientially yet.