News website The Digital Texan reported that court documents showed Plus SMS executives had made threats against Mr Tiensch's life, with one writing in an email:"Put a bullet in Les and Chris (Tiensch)."
Another email said: "Put a bullet in Tiensch."
Mr Tiensch had been on a fishing trip in Port Aransas when he was reported missing on September 11 after his wife had not heard from him.
Police found his wallet and personal items untouched in his hotel room and his Range Rover in the parking lot.
An aerial search found him on the remote island which was only accessible by air or boat.
Police are treating his death as homicide and have ruled out suicide.
"In order to preserve the integrity of the investigation, details about the location of the injuries, type of weapon, ammunition and number of shots will not be released," police chief Scott Burroughs said in a release to US media.
Family friend Dinah Welsh said the family was "devastated".
"He was a good and decent man, an incredible husband and father who will be dearly missed," she told the Austin American-Statesman.
Mr Tiensch loved the outdoors and was an experienced mountain climber, having climbed Mt Everest and Mt Kilimanjaro.
Mr Tiensch joined Plus SMS in 2006, just months before it declared it had made unrealistic statements and a Securities Commission investigation was launched.
He argued in court that the directors had persuaded him to mislead the public to inflate stock prices, and was ousted when he refused.