You suffer a -1 Penalty to attacks with the Off-Hand
Locating this was not straight forward because the information was not where I would have expected it to be. But, I don't have the final release version of the rulebook with me; I put this together from the In-Dev version that I do have with me. So, the final version of the Exalted 3 rulebook may have this oversight corrected and put the penalty in the correct place, with the normal rules for Dual-Wielding.
First, we have the normal rules for Dual-Wielding
Characters can wield one weapon in each hand as long as both weapons
lack the two-handed tag. Even with a weapon in each hand, characters
can still only make a single attack on each turn. However, if the
character is wielding a different weapon in each hand, she is free to
choose between the weapons and their associated tags each time she
attacks or parries, and may stunt her attacks and defenses however she
wants, as with a Crane stylist defending with her hook sword’s Parry
value while describing her blocks as performed with her war fan.
Characters who dual-wield two identical weapons gain a +2 bonus to
Clash attacks. “Unarmed” is considered a single weapon.
But this doesn't specify any sort of modifier to using your offhand weapon. However, if we look in Merits, we see this:
Ambidextrous (• or ••)—Innate The character doesn’t suffer a -1
penalty to actions using his off-hand.
This clearly implies that attacks using your off-hand suffer a -1 Penalty, by stating that you don't take said penalty.