When he refused, he was sacked by Chabane, and he told the commission that the then minister told him he was acting on Zuma's instruction.
When Zuma testified at the commission earlier this year, he said Chabane was name-dropping when he told Maseko he was acting on the former president's instructions.
Simons said, "I developed a very good relationship with the minister. He would often open up and have deep discussions. He knew I was an active member of the ANC at that stage so we would have political discussions as well.
"One of the discussions we had with the minister was that he touched on the issue [of Maseko] because he knew I came from GCIS. He thought GCIS was not moving in the right direction."
Simons said Zuma was "not truthful".
"When the former president said the minister was name-dropping, that is totally contradictory to the character of the minister," he said. "I thought the former president was not truthful when he, in front of the commission and in front of citizens, said the minister was name-dropping."
Simons said in March 2014, during an official visit to Australia, Chabane told him about the incident.
Jacob Zuma 'lied to state capture inquiry' - former chief director
A government official has accused former president Jacob Zuma of lying to the state capture inquiry.
Former chief director in the office of the minister in the presidency, Brent Adrian Simons, who appeared before the commission on Monday, said Zuma lied when he said he did not instruct then department minister Collins Chabane to axe government communication and information system (GCIS) boss, Themba Maseko, in 2011.
Maseko, one of the first people to testify before the commission last year, alleged Zuma had instructed him to help the Gupta family in 2010. After numerous attempts by the well-connected family to meet him, Maseko said he yielded to their request.
On the day he was due to meet them, Zuma is alleged to have instructed him, in a phone call, the help the family. Maseko said at the meeting, one of the Gupta brothers ordered him to direct the GCIS's entire R600m media advertising budget to the family's media interests.
When he refused, he was sacked by Chabane, and he told the commission that the then minister told him he was acting on Zuma's instruction.
When Zuma testified at the commission earlier this year, he said Chabane was name-dropping when he told Maseko he was acting on the former president's instructions.
Simons said, "I developed a very good relationship with the minister. He would often open up and have deep discussions. He knew I was an active member of the ANC at that stage so we would have political discussions as well.
"One of the discussions we had with the minister was that he touched on the issue [of Maseko] because he knew I came from GCIS. He thought GCIS was not moving in the right direction."
Simons said Zuma was "not truthful".
"When the former president said the minister was name-dropping, that is totally contradictory to the character of the minister," he said. "I thought the former president was not truthful when he, in front of the commission and in front of citizens, said the minister was name-dropping."
Simons said in March 2014, during an official visit to Australia, Chabane told him about the incident.
"What he indicated was that the president had instructed him to get rid of Maseko. We had a discussion and his views were that, at that stage, he thought GCIS was functioning optimally. And Maseko was giving excellent leadership at that stage," Simons said.
"He said the former president was saying to him very directly that Maseko had to be replaced. He [Zuma] mentioned the name of [former GCIS head Mzwanele] Manyi as well. There were members of staff who were present when that telephone call came."
Simons headed the Western Cape division of the GCIS when Maseko was axed.