The way i understand extra Damage such as on that weapon works like this:
when you hit the mob it does a resistance cheak against the type of extra damage <Cold , Fire , magic etc> if the mob passes then the weapon hits as a 10 Dmg weapon, if it fails then it hits as a 13 Dmg weapon. There would i imagine be partial resists aswell.
Note: i Believe Bane damage works differently but i have never parsed it so i couldn't tell you for sure.