The rennet incorporation approach actually differs with the size and shape of your container, but the underlying principles are the same. Specifically, you must stop the movement of milk before coagulation begins.
If you swirl the rennet in, you would need to counter-swirl in order to stop it and bring the milk to rest. In the meantime, the micelles are forming longer and longer strands to make curd. Kinetic motion at the molecular level result in a non-uniform coagulum. That is, if the milk is moving while it coagulates, you will have pockets of whey and possibly cracks. This in turn results in uneven curd because when you cut the curd, the water volume in each piece may differ. And then when you cook the curd, the whey loss rate will differ. And when you press the curd, you may have pockets with higher water content. Also, you may have bleaching due to acid pockets.
With cheese, all small changes in time, process, ingredients are compounded over time.
It's not the end of the world if you stir in a circle, but make sure you stop the milk movement as quickly as you can. Or, just stir up and down
BTW, rennet addition and stirring can take as long as 5 mins in large vats. Key is to distribute rennet evenly with as little movement as possible.
