Other emails show Jack and senior managers discussing Facebook posts by councillors and whether they could be used to bring code of conduct breaches against them.
This included the use of a council-owned image of the new pool by councillor Api Tapine in a post questioning whether proper consultation had been carried out.
In another email, Jack asked for legal advice on whether McGrath had breached the code or any other policies after he posted a link to a Givealittle fundraiser for The Friends of Onekawa Aquatic Centre, which is taking legal action against the council over the proposed pool.
Another post by McGrath that drew managers' attention included a picture of dirty water with the caption: "My water today. This would be why we need to prioritise drinking water over swimming pools."
The surveillance of their Facebook posts is being described by the councillors as "disturbing" and "creepy".
"I feel very uncomfortable about council staff trolling through my Facebook pages looking for code of conduct breaches.
"It's creepy," Boag said.
"It seems very inappropriate to me that staff are being employed by us, ratepayers, to spend time tracking through Facebook pages ... without us even knowing it. How can I work in a climate of trust when this is happening?"
McGrath said it was not appropriate conduct for council staff.
"It just looks like anyone who had a differing opinion on the swimming pool was being targeted.
"I don't think it's appropriate for council to be doing it. I would have thought there were more important tasks to be done in the day like sorting out the water and perhaps not spying on councillors."
The emails showed it was time for a shake-up at the council, Tapine said.
"There was clearly some strategy to negate my ability to participate in conversation.
"That's really a concern. It speaks to an environment within the governance and management of Napier City [Council] that is unhealthy, especially when directives such as this can go unchallenged," Tapine said.
There needed to be a focus on the council's management to ensure this culture changed, he said.
Wise said she found the Facebook surveillance "disturbing" and believed council's management had taken the interpretation of the code of conduct "too far".
"I've been threatened with [a breach] on several occasions but it's never been followed through with. As councillors it is important we understand exactly what we can and can't do so we can push back on that when we're told we are in breach when in fact we are not."
Jack is currently on holiday and acting chief executive Adele Henderson declined to be interviewed by RNZ.
"Elected members have standards of behaviour expected from them in the exercise of their duties as a Councillor.
"These are set out in the Code of Conduct for elected members, which are self-imposed as councillors adopt these protocols when first elected," she said in a statement.
"There is no active monitoring of councillor social media pages. However, where published articles are brought to our attention we have an obligation to investigate further, as has happened in this instance."
No concerns had been raised about the social media activity of any of the six councillors who voted in favour of the pools, council documents showed.
One of those included councillor Keith Price, who said he was not worried about his Facebook page being monitored by staff.
"I'm happy if they check mine," he said.
But surveillance of councillors' social media activity was a worry, Victoria University law professor Dean Knight said.
"It raises eye brows and is verging on stepping over the line, beyond the usual neutrality we expect of council staff and officers."
It was also troubling the council's code of conduct was being used "as a weapon" against elected members who disagree with staff, he said.
"If code of conducts are used to suppress half the conversation, the squeaky wheel, the uncomfortable naysayer, then we have an impoverished form of democracy," Dr Knight said.
Acting Napier mayor Faye White was also on holiday and acting deputy mayor Claire Hague declined to comment.
All work on the proposed new pool, including the tender process, has been halted until a new mayor and council is elected in October.
- RNZ
