Im not sure what you mean? He's not singing before 2:40 and then he sings @ 2:40-2:44 "Li-vin' on a pra-yeeer" and mouth follows the melody precisely. And solo follows right after the line.

Maybe you had youtube-related sync problems?

But talking about singing: he has very WEIRD "technique" it seems. On this video, Jon's very focused (eyes closed etc.) and it sounds almost in-tune (bit flat) & ok, but singing comes out very thin and it looks like a struggle for him all the way through. He's using the "MTV acoustic 1989" melody for many parts (which is lower than the original) and there's just some very odd feeling in his performance.