They finished bottom in 2014/15 , 8th in 2015/16 and 2nd in 2016/17 . Vieira only took over in Jan 2016 so I think he has done OK without really knowing if it is just investment or him that has made the difference.
Not quite correct. MLS has a weird structure where the overall points leader gets an otherwise meaningless trophy, as the title is awarded after a postseason knockout tournament. The top six sides from the Eastern and Western Conferences make the playoffs.
NYCFC started in 2015 (here in America, the season runs from March through October, with the playoff final at the beginning of December). They finished 17th of 20 teams. Their manager was sacked, Vieira replaced him, and they improved to 4th of 20 in 2016, qualifying 2nd out of the Eastern Conference. They lost their playoff tie 7-0 on aggregate to runners-up Toronto FC. Of note, their defense was much the same, but they scored about 25% more goals.
They again finished 2nd in the Eastern Conference in 2017 under Vieira, this time with a much better defensive record. They were 2nd in the overall points table, but again lost their first playoff tie after losing the first leg 4-1 (down 1-0 before a red card).
A lot of the improvement from 2015 to 2016 came from Frank Lampard scoring 12 in 19. The defensive improvement from 2016 into 2017 is harder to track, but maybe that comes from not playing Pirlo+Lampard together in midfield.
The main problem with MLS, and what makes it so hard to gauge, is that it's run by retirees from Europe and League One-standard players. (Bradley Wright-Phillips won the Golden Boot in 2016.) I expect NYCFC won't have the same success this season. Pirlo retired, and Jack Harrison was bought by City, leaving them an aging David Villa and not much else in attacking positions.