India lost the first ODI by eight wickets to hand West Indies a 1-0 lead in the three-match series.
The incident took place in the 48th over of India's innings, when Jadeja went for a quick single but the fielder affected a direct hit at the striker's end.
On-field umpire George did not give out out though Jadeja was short in the crease as replays would later show.
The umpire then went upstairs after the run-out was shown on the big screen and that raised question on the timing of the referral upstairs after the ball was dead.
West Indies skipper Kieron Pollard came up to umpire George as did all-rounder Roston Chase who had casually appealed after seeing the replays.
Kohli was seen walking towards the field angrily. Kohli, however, did not enter the ground as Jadeja walked back to the dressing room.
India rode half centuries from Shreyas Iyer (70) and Rishabh Pant (71) to post 287/8 after being asked to bat first on a slow wicket. But Shimron Hetmyer cracked a career-best 139 while Shai Hope scored an unbeaten 102 as the West Indies romped home with 13 balls to spare by putting up 291/2 in 47.5 overs.
Praising Hetmyer, Pollard said: " We know the talent that he has. He has been struggling a bit in the last 9 months and he has been under a lot of pressure. We just want to make him understand about his role in the side. He has been in the team from the last 18 months so he has a taste of international cricket. As a management we are very happy about his knock."
"Everyone playing should be accountable and responsible as you are playing for your team. (Sheldon) Cottrell has a magnificent last 18 months. With experience comes confidence and Cottrell is bowling superbly for us. We have talent in the caribbean we need to give opportunity to the players," he added.
Cottrell picked up two wickets, that too in the seventh over getting the backs of heavy-weights Kohli and Rohit Sharma.