Seems to me like the damage bonus Archers have with missile weapons is not being applied when having Tansheron's bow equipped (I assume the same goes for Shortbow of Gesen). Likely because they have the "attack type" set to 'projectile' instead of 'bow'. Changing the attack type on Tansheron's bow to 'bow' makes the Archer bonus work again but it will no longer fire the "ghostly arrows" and will require ammunition to be used.
It's easily reproducable by taking a, for example, lvl 9 Archer and switch between Tansheron's bow and a normal Shortbow with normal arrows equipped. The difference between the damage minimum and maximums should be exactly 3. In the little box that lists sources for all damage the "Missile Adjustment" will be listed even if Tansheron's bow is equipped but seemingly not applied.