To be fair, NewSpock wouldn't know the conditions under which PrimeSpock had encountered Khan...or -if- he had...until he asked.
Even if there's absolutely nothing useful to be gained, it's still stupid not to at least ask.
And will he do that for every villain?
"Do you know, by any chance, John Harrison? He's shooting our ship to bits and pieces."
"No, I don't. Live long and prosper."
"How dare you!"
nuSpock ONLY contacted oldSpock because the audience knows that oldSpock knows Khan. That's breaking the 4th wall. He could have just as well turned to the camera asking the audience directly.