In an article published Thursday, People.cn highlighted stricter rules for the cross-border transmission and use of investor data under China’s new laws, which take effect on Nov. 1. People.cn is a website run by the People’s Daily, the Communist Party’s flagship newspaper.

In U.S. trading Thursday, American depositary receipts in Futu and Up Fintech fell 12% and 21%, respectively.

Shares in both companies have swung wildly this year, as a wave of investor optimism buoyed Chinese ADRs, before being replaced by gloom as Beijing pursued regulatory crackdowns on areas such as e-commerce, private tuition and videogames. Futu’s ADRs have plunged 61% to $73.81 from a closing peak of $191 earlier this year.

The duo said they had moved quickly in 2019 to fix problems identified by a task force on app regulation and had more recently been studying the pending law on protecting personal information.

“We have always regarded legal compliance as the lifeline of the group’s operations, and the firm attaches great importance to personal information protection and data security,” Up Fintech said.

Likewise, Futu said it had always made data protection a priority. “Futu has been strictly complying with relevant laws and regulations. Going forward, we will continue to actively cooperate with regulatory authorities to better safeguard personal information,” it said.

In August, Futu, which is backed by Chinese gaming and social-media company

Tencent Holdings Ltd.

, said that it had just over one million paying customers as of the end of June. Its trading volume for the three months to June more than doubled to the equivalent of $167 billion.

Up Fintech, which uses the name Tiger Brokers in the Asia-Pacific region, had about 1.6 million customer accounts, including about 529,000 customers with deposits, as of the end of June.

Write to Anniek Bao at Anniek.Bao@wsj.com