Cyrillian Christology says that the hypostasis is the acting subject. In other words, persons, not natures act. This safeguards against Nestorianism, and rightly so.
We have a tension in modern Christology, though. Moderns speak of natures as self-actualizing subjects. According to McCormack, the 6th Ecumenical Council moved away from some themes in Chalcedon by positing two wills. While Cyrillians would still say that yes, there are two wills in one nature, but it is still the Person doing the willing. But which nature is being willed? Or, which will is currently employed? The problem is that the one divine person is doing the action, yet it also appears that sometimes not all of the divine person is involved in the action.
This refutes neither Cyrillian Christology or dyotheletism, but it is a tension that moderns have rightly pointed out.