Since Exalts are laser-targeted and can't rangefind, they won't reliably autofire if not facing the target. If manually fired without a laser-lock on the target, they will default to LRM-mode which is slow and low damage, which isn't very good for capitalizing on overloaded targets. I would recommend using other missiles for mounts that you don't intend to have facing the enemy, like good old harpoons.
It should be noted that Sylphon ships aren't designed to have their missile mounts used with sylphon-specific missiles alone. There are already many missiles out there that all do similar things to harpoons so adding yet another notHarpoon felt somewhat pointless.