The most common and most likely answer to this crossword clue is the 9 letter word INVERSELY
I've seen this crossword clue in The Sunday Telegraph
I
N
V
E
R
S
E
L
Y
Buddy explains!

The straight part
We know that "in contrary fashion (" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case in contrary fashion ( = inversely.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does INVERSELY mean?
INVERSELY adverb- In an inverse order or manner; by inversion.