Is “release one’s butt cheeks” a euphemism?
Solution 1:
As you surmise, when entering a possibly confrontational situation, it's not unusual to transfer some of the psychic tension to your, um, pelvic core -- to clench your butt cheeks. When the mental tension eases, you might unclench. That's what's being described here, not farting as suggested by another comment.
It's not literally true that she "manually" released the tension. She's a comedy writer, that part is for effect.