Does it work with a turret?

It works with a turret, but it still only affects things which are inside the arc(s) printed on the ship's base token. It's never 360.

Is that stated somewhere in the rules or a FAQ?

Page 19 of the Rules Reference.

Turret Primary Weapon: A ship with a turret primary weapon still has a printed firing arc that is not 360º.

NO ship (as of yet) has a 360 arc. All ships have a forward arc, and some have Auxiliary/Special arcs (behind or sideways).

All primary and secondary turrets do is let you fire OUTSIDE your arc/s