Projectiles do not inherit ship momentum. At least those fired from ship-mounted weapons.
Hand weapons are supposed to inherit momentum, but someone checked and they actually don't
In the video it could be lag as well - as you see those detached shoots on other peoples ships.
Physics engine has some problems as well. IIRC it got fixed, but players used to get killed by their own ship weapons. But it was mostly related to player hitbox lagging behind the ship, rather than muzzle lag. That one is precise enough to safely place weapons internally, with just tip of barrel sticking out.