Ms Lin claimed she had had to pay $6000 in "guarantee money" before starting work, as a kind of bond.
She also claimed to have effectively paid for her own wages - having been told to hand over $2500 to the newspaper each month.
She wanted the authority to order that she be repaid just over $63,000 in lost wages.
Authority member Ken Anderson said the case was "among the most difficult that I have ever had to determine" because of factors including language barriers and conflicting and unreliable evidence.
"I have made findings that [Ms] Lin was required to pay the sums of $6000 and $5000 respectively to New Times and/or Ms Zhou [Sandy, the managing director], as shown by tangible or probative evidence that this was so. Orders have been made accordingly."
The authority ordered New Times Press to pay Ms Lin a total of $11,000, while managing director Ms Zhou was ordered to pay Ms Lin a total of $8000.
Mr Anderson also ordered that both the newspaper and Ms Zhou pay penalty fines that totalled $14,000, which would be paid to the authority and subsequently paid to the Crown.
Mr Anderson said there was a lack of substantial evidence to show that Ms Lin had made payments to the sum of $63,165.
He therefore ruled that her claim for reimbursement of that amount was not proven.
