It's pretty easy to see how angular velocity is inherited. Get on a gat on a Squid, then have the pilot turn left, then switch right. You'll see that you have to do the opposite of lead a target when turning (lag, I guess). Bullets inherit the velocity of the ship. For example, if you're firing off the side of a moving Squid, without drag, the bullet will hit as if the Squid were motionless, provided there's not massive acceleration (which refers to both getting faster and getting slower).
It seems like the algorithm translates the angular velocity of the ship into a sideways vector for the projectile/ray. However, simply turning a ship doesn't make a gun that casters freely suddenly wing its shots off in the same direction as the ships rotation, and certainly doesn't make the projectile fire further in the direction of rotation than the gun is pointing when the projectile leaves the barrel. This also appears to be similarly true for climbs/descents while firing. Again, you should never have to lag a target.