Tengu - Paired Weapons and Beak, Attack Mods

[Max Sharpe]

Tried doing a search for this and didn't see it.

When a Tengu fights Two Weapon Style, does his Beak attack suffer the Two Weapon Fighting Penalties that are assigned to the Primary Attack in addition to the usual -5 for Secondary?

Example.

1st Level Tengu Fighter, 16 STR, 2-Bladed Sword, Two Weapon Fighting Feat.

Main Hand Attack +2 (+1 BAB, +3 STR, -2 TWF)
Off Hand Attack +2 (+1 BAB, +3 STR, -2 TWF)

Beak Attack -1 (+1 BAB, +3 STR, -5 Secondary)
/or/
Beak Attack -3 (+1 BAB, +3 STR, -5 Secondary, -2 TWF on Primary Attack)

[Winterwalker]

RAW:
Creatures with natural attacks and attacks made with weapons can use both as part of a full attack action (although often a creature must forgo one natural attack for each weapon clutched in that limb, be it a claw, tentacle, or slam). Such creatures attack with their weapons normally but treat all of their available natural attacks as secondary attacks during that attack, regardless of the attack’s original type.

Also:
Secondary attacks are made using the creature’s base attack bonus –5 and add only 1/2 the creature’s Strength bonus on damage rolls. If a creature has only one natural attack, it is always made using the creature’s full base attack bonus and adds 1-1/2 times the creature’s Strength bonus on damage rolls