An information sheet given to families in South Africa participating in the trial said the vaccine had been tested on animals and humans and was "safe and effective" in animals.
Professor Jimmy Volmink, dean of the Faculty of Medicine and Health Sciences at Stellenbosch University, told the Daily Telegraph the information sheet did not appear to reflect the monkey study, which was "not right".
Almost 1500 babies in South Africa received the new jab and parents were paid around £10 to take part. The South African regulator that approved the trial admitted that the information sheet given to parents "could be construed as misleading".
The scientists at Oxford who carried out the trial maintain the jab was safe for children and their experiment was approved by several regulators in advance. They said they followed the infants' development for two years after the immunisation was given - a time period approved by regulators.
The monkey study that concerned Beverley began in November 2006 and the application to test the vaccine in the Western Cape was submitted 18 months later. Around this time, Beverley said he heard that the animals in a study had to be euthanised "rather rapidly".
All the monkeys were infected with TB, but one group was given the widely used BCG jab, a second was given no immunisation and a third was given BCG plus the new vaccine.
The baby trial began in July 2009 and almost half of the 2800 infants taking part were given the new jab. In 2013, the outcome of the infant trial was announced and concluded that the new vaccine offered no extra protection.
Beverley, a principal research fellow at Oxford until 2010, complained formally to the university. An inquiry concluded that, although there had been no wrongdoing, it "would have been good practice for the potentially adverse reaction observed in the monkey experiment to be reported to the authorities in a more timely fashion".
Professor Helen McShane, one of the lead scientists who developed the new vaccine, has said that the purpose of the monkey study was to "test the aerosol delivery" to the animals, not to "yield safety information".
She said it was a "failed experiment" because "there was no difference" between the groups. She also told the Telegraph that there was no delay in providing data from the monkey experiment to regulators.
McShane said she did not think that families were exploited and said regulators had signed off the information sheet that was given to parents. She added that the monkey trial contained a "limited" number of animals.
South African Medicines Control Council, one of the regulators that approved the trial, said that a "large body of data" - apart from the monkey experiment and which included previous human trials - was considered as part of the approval process.
It also said that the monkey experiment was "not a trial of the vaccine in monkeys" and that "there was no suggestion that the vaccine was unsafe in the monkeys or that it had caused disease or death".
However, in terms of the information sheet, the regulator said, "In retrospect the information on efficacy achieved in the animal studies could be construed as misleading", although the "evidence of safety in the previous human studies was fairly reported".