He phoned up in May 1981 to discuss his impending arrival at Edrington business Robertson & Baxter with former finance director Ken Cameron. Mr Hunter, who has just retired as group finance director of Edrington after 33 years with the group which now has The Famous Grouse, The Macallan, Highland Park and Cutty Sark brands, recalls that a letter arrived shortly afterwards from his new boss.
He recounts Mr Cameron's "lovely letter" as follows: "When you phoned yesterday, I hadn't read The [Glasgow] Herald, and I hadn't realised you had been accepted for another appointment." The other appointment cited by Mr Cameron was Mr Hunter's engagement to future wife Christine, the announcement of which had been in The Glasgow Herald.
Mr Hunter says: "It was typical of the personal touch."
It was also in The Glasgow Herald that Mr Hunter saw the job at Robertson & Baxter advertised. The advert made it clear the company was looking for a long-term commitment.
Recalling the small advert, Mr Hunter says: "It was, 'Robertson & Baxter Ltd: young chartered accountant wanted'."
He adds: "The thing that sold it to me [was that it said], 'This is a long-term career opportunity leading to top management and not suited to someone merely seeking experience of industry'.
"Even then, I had a desire not to go off and work for ten different companies. I didn't want to be an accountant for a mega-corp."
Mr Hunter, who joined Robertson & Baxter from accountancy firm Arthur Young, speaks fondly of Mr Cameron.
He says: "Ken was the loveliest boss you could have had. He was a pre-technology finance director. What he could do with 14 columns on an A3 pad, and a calculator."
Mr Hunter, who took up the group finance director post at Edrington in 1994 and retired on June 30, is quick to praise the efforts of those at the Scotch whisky group with whom he has worked over the years, including long-time leader Sir Ian Good and current chief executive Ian Curle, as well as his first boss.
The chartered accountant, who is being succeeded by AG Barr finance director Alex Short, comes across as modest and a touch self-deprecating. However, Mr Hunter has played a pivotal role in Edrington's transformation in recent decades into a truly global player in the Scotch whisky sector, with the company continuing to be controlled by a charitable trust set up by the three Robertson sisters back in 1961.
Crucial to this transformation was Edrington's £601 million acquisition in 1999 of then stock market-listed Highland Distillers.
Mr Hunter, who appears fairly laid-back, recalls the major and complex exercise of consolidating the accounts of the interwoven corporate entities involved in the Highland deal to show what the enlarged business would look like afterwards. He declares that the work on the Highland deal was "very stressful at the time", recalling how he pored over his spreadsheets at home with a nagging worry that there might be something huge that he had not taken into account.
There was no such omission, and the Highland deal has worked out fantastically for Edrington.
Mr Hunter says: "We went out and borrowed £500 million. It was terrifying, and turned into complete triumph."
He has also played a key role in arranging and managing Glasgow-based Edrington's international distribution operations and alliances over the years. This work has gone a long way towards enabling Edrington to achieve the international clout from which it is now benefiting, with its latest financial results showing an underlying pre-tax profit of £174 million in the year to March 31. This was up from £168.6 million in the prior 12 months, and way ahead of the company's pre-tax profits of £118.6 million in the year to March 2010.
Well aware of what is involved in selling into overseas markets, Mr Hunter says he worries about some of the raft of new Scotch whisky distilleries being set up in Scotland with the help of public money. He adds that making the whisky is the easy part, while selling it in 10 to 12 years' time is the difficult part.
Mr Hunter believes it is important in life to focus on what lies ahead, rather than looking back and having regrets.
The retired finance director lives in Killearn in Stirlingshire with Christine, a doctor who has just retired from general practice, and they have three grown-up children, Louise, Emma and Andrew.
Mr Hunter says of his retirement: "It is a new stage of life. I don't want to get too philosophical. I am a great believer in looking forward to what is next."
Noting that "if you are lucky enough to have kids, they stop being cuddly babies", he highlights his belief that, instead of worrying about that, it is important to realise that "every stage is nice", as children go on to school and then on to university and jobs, and get into relationships.
Mr Hunter emphasises he has no regrets about not getting the chief executive post at Edrington when Sir Ian handed over that part of his role in 2004 and became non-executive chairman. He is satisfied the report from the lengthy psychometric test which formed part of the interview process for the top job summed him up fairly well.
Self-deprecatingly, he says: "I am a finance director. I have loved it. I have been an okay finance director. I would almost certainly have been a hopeless chief executive. Ian Curle has been a superb chief executive."
And Mr Hunter cannot talk highly enough of the culture at Edrington, and its people.
He says: "We really don't do people with a side to them. If you ain't as you look in Edrington, you will be fint oot. We have our moments of disagreement [but] we all get on... We have a lot of fun in Edrington. I do think it is one of the secrets of success, the way the whole board and the broad raft of people have a laugh, but we are serious about the business."
Mr Hunter, who speaks French and started learning Spanish around 2005 when Edrington was in talks with Brugal about buying into the Dominican Republic-based rum producer, is also passionate about the huge but low-key donations made by the charitable trust which controls the Scotch whisky company.
The Robertson Trust, which receives about three-quarters of the dividends paid by Edrington, donated £15.3 million to Scottish charities in the year to March 2013.
Mr Hunter also highlights the recent move, in which he played a key part, to introduce substantial charitable giving by Edrington's overseas operations, in which more than 60 per cent of the company's near-2,400-strong workforce is employed.
This has involved Edrington, over the past couple of years, putting aside about one per cent of its pre-tax profits for charitable causes overseas. Mr Hunter notes this amounts to about £1.7 million a year, and highlighted donations made in the likes of Asia, Africa, Scandinavia, the US and Caribbean, including money given to a women's refuge in Sweden and the provision of laptops for African schoolchildren.
He also highlights the fact that Brugal's executives had, for the first year, paid the salaries of staff at the new George Arzeno Brugal school in the Dominican Republic out of their own pockets.
Mr Hunter, while he will clearly miss his colleagues, has no regrets about retiring at the age of 59.
Revealing he had agreed his exit plan with Mr Curle well in advance, Mr Hunter says: "It meant I had a year reflecting on the change that was coming. I never really had an anxious moment about it, to be honest. I had a very happy time at Edrington. I am very happy to move on to see what life brings.
"We get this life: childhood, education, working, retirement. A lot of our best friends don't get to retirement. You are going to get some unspecified period, if you are lucky, to retire. If you are lucky enough to have your pension sorted, you should get on with it."
While emphasising he has enjoyed his career, he adds: "I have spent my life working flat out. It is the totality of your life. I am realising now, after only six weeks, how many things I want to do."
Mr Hunter is a keen sailor and joined the Commonwealth Flotilla last weekend. He is also passionate about his role as convener of the Court at the University of Strathclyde, to which he was appointed in August 2012.
Mr Hunter also likes fishing, although he points out he has not had many opportunities to pursue this passion over the years.
He says: "I own a small, muddy bit of river out in Stirlingshire that gets salmon up it once a year."
Noting a ban on fishing salmon on a Sunday, the length of the season, and the fact that it has had to be raining beforehand, Mr Hunter declares: "For the last 15 years, I should think I have got fishing once a year."