Ok. The way i read it is tactician only works in arc. Ships like decimator and falcon have turrets that can attack ships outside their fire arc. So this means the target must be in front for tactician to work. Correct?

Ok. The way i read it is tactician only works in arc. Ships like decimator and falcon have turrets that can attack ships outside their fire arc. So this means the target must be in front for tactician to work. Correct?

Correct!

Decimators/Falcons have a standard firing arc, and can shoot outside it. Tactician only works in the arc.

Firesprays/Hounds have Auxiliary arcs, which do count for Tactician.

Remember that Tactician works for ALL arcs. So, it will work for the auxiliary arc on the Firespray too.