Two weapon penalties are mitigated by use of the two weapon fighting feat and if the weapon is light.
Rapiers are not light weapons, however you can use your dexterity for the attack modifier instead of strength if you have the weapon finesse feat, even though the weapon isn't light.
Two weapon fighting gives you one extra attack per round with your secondary weapon, modified from the primary attack bonus.
Circumstances Primary Hand Off Hand
Normal penalties –6 –10
Off-hand weapon is light –4 –8
Two-Weapon Fighting feat –4 –4
Off-hand weapon is light
*and* Two-Weapon Fighting feat –2 –2
Improved Two Weapon fighting adds a second attack for their offhand weapon at -5, again modified by their primary attack bonus (and any other TWC modifiers)
So; running through the numbers;
The characters base attack is +13/+9.
The two weapon fighting feat gives a penalty to the primary attack of -4. Main attack is now +9/+5.
Two weapon fighting extra attack is at +9 as per main attack (ie the same -4 modifier), this gives +9/+9/+5.
Improved two weapon fighting adds an additional (Second) attack for the secondary weapon (currently at +9) at -5, (ie in addition to existing -4 penalty for the second weapon)
So this makes +9/+9/+5/+4 (Or +9/+9/+4/+4 if their attack mod is actually +13/+8)
With a light offhand weapon these modifiers would be:
+11/+11/+7/+6 (Or +11/+11/+6/+6 if their attack mod is actually +13/+8)
Quite the chainsaw.