Recently, I got a review back taking me to task for not putting spaces on either side of em dashes. This always looked wrong to me as well (and I always have to go back into the text after finishing and edit it it make it so, because Word autocorrects it). BUT: Your styleguide specifically demands that we don't separate the em dashes with spaces from the words coming before and behind!
Under the punctuation rules (not preferences) there is this exact example sentence:
"He made it his mission—his one and only mission—to tell them about what happened."
Either fix the guidelines or tell the reviewers not to dedact points from translators who go out of their way to follow them!