''It was agreed that staff in Dunedin who did not attend work on Wednesday, 7 October 2015, need to record this as annual leave,'' the email read.
''This approach ensures overall fairness for those staff who did attend work and for those who did not.''
The threat was posted alongside a picture of a gun on online messaging board 4chan.
The anonymous post warned against going to the campus on Wednesday, October7.
A gunman who killed 10 people at a United States university earlier this month used 4chan to warn of his plans.
Police said they were taking the threat seriously, and the university encouraged lecturers to put course information online, to accommodate students who chose to stay home.
The university declined to respond directly to a series of questions, instead providing a statement from human resources director Kevin Seales that largely echoed the October 13 email.
''On the day in question, the university was open for business in the usual fashion,'' he said.
''Staff who came to work provided a visible and calm presence for ... thousands of students ...
''We understand that some people wanted to stay home.
''However, given that the university was open, recording their absence as annual leave ensures overall fairness to all staff.''
Otago University Students' Association president Paul Hunt said the university was ''understanding of students'' on the day of the threat.
''[They] understood that students had different levels of risk tolerance.''
He estimated less than half the student population was on campus the day of the threat.
Otago law professor Andrew Geddis, who attended work on the day of the threat, called the university's approach ''odd''.
''Given that the university was very conscious that students were concerned and did nothing to insist students come to class, it seems odd that they would be taking a different approach to their employees,'' he said.
Mr Scott said the university's actions were ''punitive''.
''The staff at the university put the students at the centre of what they do ... Taking an unexpected day off is not something done lightly by people,'' he said.
''People were in a situation they had never been in before.''
To Mr Scott's knowledge, staff had not been warned they might lose a day of annual leave if they did not go to work that day.
Mr Scott said the university had a policy for extreme weather events, where staff were only required to work ''if it's safe and reasonable to do so''.
''You've got to make your best effort, but bearing in mind your safety.''
Attending work on the day of the threat should have been considered a health and safety risk, he said.
''People chose not to come to work for health and safety reasons. They were clearly concerned of a physical threat, and they were undergoing suffering from varying degrees of stress.''
It was ''a pity'' the university did not see it that way, he said.
And Mr Scott questioned the university's assertion that everything was ''business as usual'' on campus that day.
''The university wasn't open for business in the usual fashion,'' he said.
''It was an unusual day on campus.''
