What would lying on the application do you any good if you know for sure beforehand that after getting a job offer you have to get a police record anyway? They will 100% ask for it. You will 100% have to hand it over to your future employer before signing a contract.
So it will only be an issue if you can not get any police record from the states without the DUI showing,
Btw, about the part that it was just a silly thing: thank god it was just a silly thing and no-one was injured at the time. People like you set a great example on why to take rules and laws serious. So this is indeed how the system works as far as I can tell.