Cambridge Analytica’s rise has rattled some of President Trump’s critics and privacy advocates, who warn of a blizzard of high-tech, Facebook-optimized propaganda aimed at the American public, controlled by the people behind the alt-right hub Breitbart News. Cambridge is principally owned by the billionaire Robert Mercer, a Trump backer and investor in Breitbart. Stephen K. Bannon, the former Breitbart chairman who is Mr. Trump’s senior White House counselor, served until last summer as vice president of Cambridge’s board.

But a dozen Republican consultants and former Trump campaign aides, along with current and former Cambridge employees, say the company’s ability to exploit personality profiles — “our secret sauce,” Mr. Nix once called it — is exaggerated.

Cambridge executives now concede that the company never used psychographics in the Trump campaign. The technology — prominently featured in the firm’s sales materials and in media reports that cast Cambridge as a master of the dark campaign arts — remains unproved, according to former employees and Republicans familiar with the firm’s work.

“They’ve got a lot of really smart people,” said Brent Seaborn, managing partner of TargetPoint, a rival business that also provided voter data to the Trump campaign. “But it’s not as easy as it looks to transition from being excellent at one thing and bringing it into politics. I think there’s a big question about whether we think psychographic profiling even works.”

At stake are not merely bragging rights, but also an emerging science that many believe could reshape American politics and commerce. Big data companies already know your age, income, favorite cereal and when you last voted. But the company that can perfect psychological targeting could offer far more potent tools: the ability to manipulate behavior by understanding how someone thinks and what he or she fears.