ERRATUM: Wait, nevermind : you mean you are playing Fighters with the dual-wielding style. Roger.
In my combat logs, I think I saw the bonus damage on offhand even for non-Fighters (which would be an error). Will have to check some more.
I'm playing as Rogue.
And yes, I saw additional +3 (in my case) damage bonus from Dex. But i'm wondering about adding Dexterity Modifier to Attack Roll for off-hand.