"I've not heard that phrase before - am I understanding correctly it's used only by the Russian Orthodox?"
That's correct.
That's a bit of a generalization. It seems that the phrase was introduced by Peter Mohlia. Molia was Latin educated, though he preserved Orthodoxy in Ukraine he's known to have introduced many Latinized concepts. It seems the Slavic churches adopted it latter. It seems that the Serbians and Georgians also use it, as well as the Antiochians.
"The Slavonic formula of absolution, introduced by Peter Moghila, Metropolitan of Kiev ... And I, an unworthy Priest, through the power given me by Him, forgive and absolve you from all yours sins."
http://www.stots.edu/article.php?id=39
"And I, his unworthy Priest, through the power
given unto me by him, do forgive and absolve thee from all thy
sins....??]’ This prayer was introduced into our order of confes-
sion quite recently, less than three hundred years ago; neither the
Greeks nor the Edinovertsi?? have it, but it came to us from the
Roman Catholics.??
??
Ibid., p. ???.
??
Old Ritualists (Old Believers) who re–united with the Russian Or-
thodox Church, but were allowed to maintain their pre–Nikonian customs.
??
Metropolitan Anthony, Confession, pp. ?????."
http://www.orthodoxinfo.com/praxis/guidech2.pdf
also
http://www.antiochian.org/1140462230