Mr Brown's drug test came back non-negative and he was immediately suspended.
At a meeting the next week Mr Brown told his supervisor he smoked marijuana recreationally, but not at work, the ERA report said.
He was dismissed from work.
Employment Relations Authority member Anna Fitzgibbon said in her decision that Ballance did not have the grounds to request Mr Brown undergo a drug test.
She said a complaint from a member of the public wasn't a reasonable cause to make the two men submit to a drug test.
Mr Beck told the authority that Mr Brown had exhibited unusual behaviour on the day of the drug test, which supported the reasonable cause test. However, Ms Fitzgibbon did not accept this.
Mr Brown was awarded three months' lost wages, but Ms Fitzgibbon did not order his reinstatement.
She said reinstatement would not be appropriate because Ballance no longer trusted Mr Brown as an employee after he admitted to recreationally smoking marijuana at home.
He told the authority he had stopped smoking marijuana after he was suspended from work but failed to provide any evidence of this.
Mr Brown was awarded $1500 in compensation.
The authority earlier found Mr O'Connor was unjustifiably dismissed. He was awarded $10,857 for lost wages, and $3000 compensation for humiliation, loss of dignity and injury to feeling.
A spokeswoman for Ballance was not immediately available for comment.