The past few months have been a turbulent time at St Mary's, with a host of key players exiting in the wake of Pochettino's decision to take the reins at White Hart Lane.
Bookmakers dramatically shortened the odds on Saints being relegated as a result, but some fine acquisitions and the wily appointment of Dutch great Koeman has nipped such talk in the bud.
Saints sit second in the Barclays Premier League, albeit with the season in its infancy, and have won their last six matches in all competitions - a fantastic start fans' favourite Le Tissier praised Koeman for.
"I was well chuffed when his name got linked with the job and saw that he was interested," he said
"He's been a revelation for us so far.
"He's very calm
I've met him a couple of times already and he's a very calm, very assured manager
He's not one that will flip his lid at the sign of the first problem.
"He has dealt with things in a completely professional way and I like the way he carried himself
Long may that continue."
Next up for Saints is a mouth-watering clash with Koeman's predecessor Pochettino, whose new side head into Sunday's match eighth in the standings.
"It is a new era," Le Tissier said
"It's a chance, probably for the fans more than anything, to say to the manager 'ah, you made a mistake in going because we are doing better than you are at the minute!'
"Listen, it is still early days
I'm realistic enough to know that and not get carried away but it has been a brilliant start.
"We don't get these moments often so we should enjoy them while they are there."
Le Tissier was speaking after signing up for Prostate Cancer UK's 'Men United v Prostate Cancer' campaign.
The former England international lost his father-in-law to the disease 17 years ago and his driver, Dave Hills, was recently diagnosed with it.
"I've experienced it a long time ago and Dave's diagnosis has brought it to my attention again," he said.
"Awareness is the biggest thing about it all and getting people to spot the symptoms early enough and get checked out on a regular basis.
"Prostate Cancer UK have done a great job with their Men United campaign and reached a lot of people that perhaps would not have been in range in the past."
Source : PA
Source: PA