Pretty sure its reviewed by the league, not the ref.
Apparently, it is a combination. The on field official reviews the play on tablet and consults with the league office. Unfortunately, calls like where the player went out of bounds or if forward progress was stopped will be determined more by the on field officiating crew:
The main problem is that the initial call will not be reversed by the league office without first consulting with the ref and what he saw as the circumstances that led to the forward progress being stopped or reached. And even then, there has to be conclusive evidence that over rules what the Ref says he saw. In the case of Hekker, everyone EXCEPT the officials saw it as a first down. I'm not sure what Vinobitch used as his argument for the call but the former vice president of officiating (title?) on the broadcast even said that it was a first down.
We've seen other calls in other games not overturned by the replay officials when it seemed pretty obvious the call was wrong. It appears to me that the league office is reluctant to over rule an on field official if he still disagrees.
“I have never had a situation where New York and I differed on what we were going to do, so it will still be seamless,” referee Brad Allen said. “The fact that in most circumstances, we’re not physically going to be under a hood, we are going to be looking at a tablet, it’s a little different.