I'd like to at least think he's the same Pavel Chekov of the TOS universe, so I guess if I had to come up with an in-universe explanation for the four year difference in age it would be a transporter accident.
It's not like transporter accidents were rare in Trek, and they did peculiar things to people and their physiology. Since all bets are off on history after the Kelvin was destroyed, maybe Pavel was born at the same time as in TOS, but at age three or four, while being transported to visit his aunt on a moon base, an accident aged him four years. He beams up a four year old, and materializes in front of his aunt as an eight year old.
Upon a thorough exam, it was found he was sound and stable in every way, but the aging could not be reversed because the "pollutants" from the malfunctioned transporter matrix buffer affected his DNA. He's still Chekov, with the same personality and ambitions, but he's a bit more intelligent and has curly hair. He also has a four year gap between his physical age and his memories.