Turrets take some time to shoot when they have a target in their range and view.
If, during that time, the target moves out of the turret's view, the turret doesn't shoot.
Rotating gives the turret more time to shoot.
Try to put a turret on a section where the target moves horizontally for some time.
(E.g. left of the second turning point of the path)
You will see that the turret shoots there.
The issue is probably the time it takes to calculate stuff for the turrets.
This isn't a bug. You will probably have to switch rotate to "on", make the targets bigger or move slower or simulate the turret behaviour with "line of sight".