The Edinburgh star has been touted as a future Lion following his try-scoring heroics for both club and country - Visser has been the RaboDirect PRO12 top try-scorer for three consecutive seasons.
"It was a good start, especially continuing winning ways with Scotland following on from Australia. It's brilliant to be able to build on that.
"From a personal perspective it was good to get two tries. It wasn't my goal to score. I just wanted to have a consistent game, which I think I managed.
"There's a lot more pressure when you're representing your country. But being able to play Fiji away from home was a good first cap. There wasn't as much pressure as there would have been in front of 65,000 people at Murrayfield."
The Scots finish their summer campaign against newly crowned Pacific Nations Champions Samoa in Apia on Saturday.
And Visser is desperate to complete Scotland's unbeaten summer, while improving on his own impressive debut performance.
"There's a lot to build on and having not played since the end of the season with Edinburgh it was good to get a game under my belt," added Visser.
"Hopefully I can show a bit more against Samoa if selected.
"Samoa are a good side. We saw them play Fiji last week and it was a good physical battle. In comparison to Fiji they are a bit more strategic and try to play in the right areas of the field."