The answer
The original definition of the Greek word Hypostasis (as used also in the Holy Book of Heb 1:3) is substantial nature, essence, actual being, reality (in contrast to what merely seems to be).St. Cyril talked about One NATURE (Hypostasis/Physis) of the Incarnate Logos. Thus St. Cyril (and St. Athanasius) did not separate the term Hypostasis from its original meaning by drawing the sharp distinction between it and the term Ousia or Physis as the Cappadocian Fathers did, which is probably what is causing the confusion here.
Therefore, 'Hypostasis' and 'Physis' were used interchangeably by St. Cyril to signify 'Nature'.
In short, when we say in the Psalmody "One nature out of two" we are referring to the Hypostatic Union which resulted in this One Nature of the Incarnate Logos.
As written in the Holy Psalmody: "One nature out of two, (1) a Holy Divinity, coessential with the Father, and incorruptible, (and 2) a holy Humanity, begotten without seed, coessential with us, according to the economy. This which He has taken from you O undefiled, He made one with Him, as a hypostasis." [Sunday Theotokia]
The book of "Nature of Christ" by H. H. the Pope explains our belief and St Cyril's in a wonderful way.
Answered by His Eminence Metropolitan Youssef (opens in a new tab)