After working at Theranos Inc. for eight months, Tyler Shultz decided he had seen enough. On April 11, 2014, he emailed company founder Elizabeth Holmes to complain that Theranos had doctored research and ignored failed quality-control checks.

The reply was withering. Ms. Holmes forwarded the email to Theranos President Sunny Balwani, who belittled Mr. Shultz’s grasp of basic mathematics and his knowledge of laboratory science, and then took a swipe at his relationship with George Shultz, the former secretary of state and a Theranos director.

“The only reason I have taken so much time away from work to address this personally is because you are Mr. Shultz’s grandson,” wrote Mr. Balwani to his employee in an email, a copy of which was reviewed by The Wall Street Journal.

Mr. Shultz quit the same day. As he was leaving Theranos’s headquarters in Palo Alto, Calif., he says he got a frantic cellphone call from his mother, who told him Ms. Holmes had just called the elder Mr. Shultz to warn that his grandson would “lose” if he launched a vendetta against the blood-testing startup.

Tyler Shultz, now 26 years old, was among several Theranos employees who tried to voice concerns inside the company about what they saw as troubling practices, and Mr. Shultz was the first to blow the whistle to a state regulator. He says he wanted to expose the problems to protect the health of patients and his grandfather’s reputation.