Hong Kong-based Students and Scholars Against Corporate Misbehaviour (SACOM) say Lens Technology, which makes touchscreen glass, used forced overtime, withheld wages and risked workers' health after a months-long investigation into three of its factories.
Company founder Zhou Qunfei, herself a former factory worker, became China's richest woman after Lens Technology's debut on the Shenzhen stock exchange in March.
As the iPhone 6s went on sale in markets including Hong Kong, Japan and mainland China today, SACOM called for Apple to "apply immediate measures to rectify exploitations in its supply chain".
The rights group's allegations include workers going for a month without a day off, wages being withheld for weeks and that the company failed to pay social security.
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"Dust, noise, polluted water and chemical substances are common problems on the shop floor," it added, with management "ignoring if workers were well-protected".
It sent undercover workers into factories, as well as interviewing workers off-site.
SACOM was due to deliver its new report on Friday to Apple and Lens Technology, based in the southern Chinese province of Hunan.
But the hundreds of customers who had pre-ordered one of the new phones were largely oblivious.
"I think bad conditions happen to all brands," said James Leung, 30, who was waiting to pick up a rose-gold phone for his wife, which he said cost him Hong Kong Dollar 5,000 (USD 645).
"For me, I need a phone, so I'll get a new phone."
Lens Technology also supplies Samsung and other leading tech firms. It primarily makes touch-sensitive glass covers for mobile phones, computers and cameras.
"But Apple is the richest and has the biggest ability to make change and bring the industry forward," she said.
"We're trying to bring the facts in front of people and let them know what they are choosing."
Lens Technology and Apple were not immediately available for comment.