"So to come out in a test and score runs again straightaway was a little bit surprising, but obviously what you plan on doing every time."
Three of the star figures in the 186-run first test win were Neesham, opener Tom Latham, 83 and 73 in his second test - and first as an opener - and debutant offspinner Mark Craig, who produced a man of the match-winning eight for 188.
Add in experienced Tim Southee's top-class seam bowling, Kane Williamson's sixth test hundred and wicketkeeper BJ Watling's strong hand with the gloves - eight catches - and the bat, with a resolute 89 in the first innings, and this was a team doing the business without notable help from usually key figures.
As for the chances of joining Indian Mohammad Azharuddin as the only players to score centuries in their first three tests, lefthander Neesham said nothing would change in terms of how he approached his innings.
"Every time you go out to bat you're planning on getting 100. I'll look to play straight the first few balls, get myself in and try to extend that as long as possible."
The Queen's Park pitch, the subject of contrasting opinions on its appearance and likely nature, was bare in patches and dry on first look yesterday, 48 hours out from the start.
The West Indies have dumped batsmen Kieran Powell and Marlon Samuels in favour of uncapped Jermaine Blackwood and Leon Johnson, who played three ODIs six years ago, while clever spinner Sunil Narine's decision to miss a pre-series training camp to play the IPL final with the Kolkata Knight Riders means he's gone for the series.
If the Windies need to win the third test in Barbados, however, we should watch that space.
Neesham's form, plus the first test result, make it hard to find a spot for the again fit Corey Anderson. There might be a case for a third specialist seamer in Neil Wagner, presumably at legspinner Ish Sodhi's expense, while the other issue to resolve is who opens with Latham.
Peter Fulton has scored just 63 runs in his last 10 innings. Forget talk of putting Anderson, or Watling or Neesham up the top. The only option is Hamish Rutherford, also out of runs.
"Neither has been bashing the door down through numbers, but we felt Peter's experience was important over here," coach Mike Hesson said.