Were all Western Rites affected by the New Roman Psalter?
According to my [poor] understanding, the only Rites of the Latin Occident exempt from the reforms of Pope St. Pius X were the Mozarabic and Ambrosian Rites, which are distinct from the Roman Rite. The Medieval Uses of local dioceses and Religious Orders were merely variants of the Roman Rite, and were not distinct Rites in the strict sense of the word. All existing Uses of the Roman Rite were affected by the new legislation, and this can be seen from the fact that the great Religious Orders that were possessed of their distinct Uses (such as the Benedictines, Calced Carmelites, Dominicans, Norbertines, Servites, etc.) had the typical editions of their Liturgical Books emended in order to conform to the new reforms (though within the limits of their peculiar rubrics and customs).
As far as I know, the Benedictines (and all related Monastic Orders) were the only ones to have kept their ancient Psalter, composed by St. Benedict as found in the Holy Rule in the 5th century or so.
It was the Anglo-Catholics who continued to recite (in the Coverdale translation) the ancient Roman Psalter, and even some of them abandoned the practice, as is seen in the Anglican Breviary published in 1955, which adopted the Psalter-schema of 1911.
In 1957, there were reforms promulgated for the Ambrosian Breviary, but I do not know the nature of these reforms. I do not know what happened with the Mozarabic Rite...