The 14-try haul gathered over the past seven weeks is a Scottish record, while their world ranking of fifth put them above the powerhouses of France, South Africa and Wales.
The task of continuing that development falls to Townsend. But Visser reckons the man who led Glasgow to the Guinness PRO12 title in 2015 has already demonstrated a game plan that will work with the national team.
He said: “I think the style will be similar under Gregor. If you look at the way Glasgow have played over the last couple of years, they play very exciting rugby. I remember when I first joined Edinburgh we used to play the exciting rugby and Glasgow didn’t. But there’s been a complete turnaround in the style Glasgow play. A lot of off-loading, a lot of backs play. It’s great to watch. Hopefully, it will be quite a seamless transition to Scotland for Gregor.”
Cotter inherited a team in transition when he took up the reins back in the summer of 2014. His first Six Nations ended in the humiliation of five straight defeats.
But he leaves for French side Montpellier with his CV enhanced. Only a controversial late call by referee Craig Joubert denied his side a World Cup semi-final slot 18 months ago, while he is the first Scottish head coach of the professional era with a win ratio of more than 50 per cent.
And Visser admits his players owe him a debt of gratitude. “He has been great,” he said. “He’s a very positive coach. He’s always wanted us to play rugby and always wanted us to score tries. He said to us that he wants us to go out there to express ourselves. Since I joined Scotland we’ve been able to do that. We’ve got an exciting back three and turned into a team that can score tries. What Vern has added is the way we approach the game, especially in our own half.
“We’re now a bit more realistic with the way we play the game. You saw that against Italy and it’s rewarding to see that in his last game.
“I like to think his style was tailor-made for the likes of me. It’s good because we have got some real pace in the centres and out wide at the moment.
“Some of the tries we’ve scored in this tournament, like Stuart Hogg’s against Ireland, where we exposed them out wide, the one I got against Wales and the one Tommy Seymour scored in the second half on Saturday, are testament to how much we’ve worked with Vern.
“Vern’s moved the team forward from us finishing fourth and fifth to now hopefully being able to finish in the top half of the Championship. His work isn’t done yet. Vern has to move on but Gregor will be trying to push it forward.
“As a squad we’re not happy either. We’re constantly trying to get better. But Vern has left the team in a much better position than when he found it, that’s for sure.”
Visser says there is a softer side to the famously reserved coach that he will miss just as much as the impact he had on the team.
“He’s quite stern – Stern Vern,” he said with a grin. “He’s a forward and I’m a back so you have that barrier. But he’s quite funny. He talks quite quietly but then you’ll walk past him and he will make a funny remark out of nothing. I always enjoyed that side of him. He’s a great guy. He’s not only moved us forward in the way we play rugby but there’s also a real team ethos in the squad now, which is a testament to him.”