In letters received since the accusations were first made public on July 8, the former staff members have written of "the unhealthy management culture", "intimidating behaviour by senior managers" and "disrespect and bullying".
A further eight letters containing accusations of intimidation have appeared on the ODT website.
Museum director Shimrath Paul has previously described the PSA allegations as "untruths" and yesterday, in a statement to the Otago Daily Times, referred to statements made by "a few disgruntled and disaffected ex-staff members".
"Naturally, if these ex-staff members have been performance managed, they will be feeling at odds with management. They are, of course, entitled to their opinions, but they need to be considered in the wider context."
One of the letters was written by former conservation officer Laurence Le Ber, who resigned in April.
"This at a time of one of the worst economic depressions. I had no job to go to, so it was not a decision taken lightly."
Mr Le Ber said five other staff members were in the process of resigning at that time.
"Of them, only one had a job lined up. All of us would rather take our chances than to put up with the disrespect and bullying."
Another former staff member, who did not want to be named, said she was proud of the exhibitions and programmes she worked on for the museum.
"The public should know, however, that these programmes do come at a cost for the staff concerned.
"Many staff, both current and former, have until now kept silent over the unhealthy management culture, which encourages workers to consistently place the museum before all else, including family."
An anonymous correspondent said he or she got "pieces of work thrown at me all the time, and I often worked overtime to complete them, and was not paid."
"If anyone even hints at not being impressed with management processes, that person is labelled a bad apple . . . That person is treated badly from that day on, until they are basically forced to quit because they can't take the bullying anymore."
Another former staff member, who did not want to be named, believed it would be easy for the Dunedin community to disregard the PSA claims as coming from one "disgruntled ex-staff member". However, she was aware of "at least nine other ex staff members" who agreed with the PSA claims.
"I am an ex-staff member who also unfortunately experienced the conditions outlined by the PSA during my time working there."
Mr Le Ber said he was expected to regularly work evenings and some of the weekend for no extra pay as it was "part of the accepted museum culture".
"Failure to do so would not be tolerated and would be seen as evidence of not being a team player.
"When I point out that this intimidation was not only illegal but would impact adversely on my family, I was told that the museum was employing me, not my family, and that if I did not like it, to move on.
"There was certainly no open door policy addressing staff concerns being offered that Mr Paul refers to. Rather, as he likes to tell his staff, you are either with us or against us."
Mr Paul said yesterday the museum was "extremely successful", attracting more than 600,000 visits per year. He attributed its success to staff.
"Otago Museum people work differently. At times, this means going the extra mile to get the job done.
"In short, the museum operates as a high-performing business. The difference, of course, between the museum and a commercial operation is that the museum team are driven not by money but by their genuine desire to make a difference for their community."
He "freely acknowledged" that the museum culture and way of working "is different and unique and that it may not work for everyone".
Museum board chairwoman Margaret Collins said she was "not at all concerned" about the PSA's concerns and had "every confidence" in Mr Paul and the museum's staff.
She said there was a "positive atmosphere" at the museum and it was a "positive workplace" which never had difficulty finding staff.
Ms Collins and Mr Paul referred the ODT to an "apology" letter the museum's lawyers received from the PSA in 1999 over public comments it made then about a staff matter.
