The most common and most likely answer to this crossword clue is the 6 plus 3 plus 6 letter word BEHIND THE SCENES
I've seen this crossword clue in Financial Times
B
E
H
I
N
D
T
H
E
S
C
E
N
E
S
More clues leading to the result BEHIND THE SCENES
- At bottom, those emotional outbursts are private
- Secretly responsible for the tantrums
- Hides ten benches needing repair out of sight
- Posterior and chest seen, sadly in secret
- Working in shed, hence best in private
- Bottom and chest seen awkwardly in private?
- Risk taking back husband with start of emotional outbursts in private
Buddy explains!

The straight part
We know that "Secretly responsible" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case secretly responsible = behind the scenes.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.