My server crashed so I had to retype this whole reply!
The word translated as “person” in the OP is likely a mistranslation (perhaps someone with the original Greek can verify?). We do not believe Christ is one person who subsists from two persons, rather one single person with a compound Theanthropic hypostasis who subsists from two natures or two individuated realities. You see, when we say that Christ united His Divinity with His humanity in a perfect, unconfused union, we do not maintain that He united the human ousia/ essence shared by all of humanity to the Divine ousia/essence shared by all three members of the Trinity. Otherwise, we would not be able to say that Christ suffered on the cross, while the Father and Holy Spirit remained impassible. Rather, He united His individuated Divine hypostasis with an individuated, soul-possessing body, thereby making His formerly singular Divine hypostasis a compound Theanthropic hypostasis.
In our tradition, ousia/essence refers to qualities belonging to all members of a class of being (e.g. the human ousia shared by all human beings or the Divine ousia shared by the persons of the Trinity). Hypostases are individuated/individual realities of ousias/essences (e.g. you and myself are “hypostases” or individuations of the human ousia). Hypostases can be self-subsistent or non-self-subsistent (more on that later). Physis/nature can mean either essence or hypostasis depending on the context.
When we speak of Christ as being “from two natures,” we mean that He is from two individuated realities/hypostases. Following the Severian/Cyrilline tradition, we maintain that there are self-subsistent hypostases and non-self-subsistent hypostases. The former do not depend on unity with any other external entity for their existence, while the latter only exist by virtue of their union with the former.
In the case of Christ, we say that His Divine hypostasis is a self-subsistent reality which does not rely on its union with the humanity for its existence. His “human hypostasis” is non-self-subsistent, meaning that it does not exist in, of, or for itself. Rather, it depends on its union with God the Word for its existence. By affirming this, we dispel both Nestorianism and Apollinarianism in the same breath, by saying that Christ’s humanity never existed outside its perfect union with the Divinity, while maintaining that his humanity is a perfect and integral reality. The Chalcedonians have a similar concept, whereby they describe Christ’s humanity as “enhypostaton.”
As an analogy, I can say that my soul is a self-subsistent hypostasis (because it does not rely on its unity with my body to exist), while my body is a non-self-subsistent hypostasis, because it depends on its union with my soul for its existence.
I hope my reply was helpful.
(the first few letters are particularly helpful)