Aren't the quads secondary ARCs though, therefore it would trigger?
Autothrusters mentions nothing about primary or secondary arcs. Merely that you are out of firing arc and outside range 2. The secondary arc on the Firespray is still an arc. The printed arcs on the CR-90 are still firing arcs. Just because the arcs on the CR-90 are only used by the secondary weapons doesn't mean they are not firing arcs.