What majortom says is accurate, but there's more.
As you said, the geometry of the servos is off.
at the neutral position, the servo arm should be perpendicular to the centerline of the two pullpull cables. Generally this means straight across the airplane fuselage. Same with the control horn, but that MAY mean that you should find a way to tilt the control horn a bit to make it perpendicular to the actual force if the fairleads are offset below the stab, for example. The cables should run straight as possible, and exit the fuselage through fairleads (low-friction guides) Each cable should attach the same distance out on the servo arms (end hole preferred). Each cable should attach the same distance out on the control horn, but this distance does NOT have to be the same distance as it was at the servo.

Here's the trick part: If you draw an imaginary line through the holes you use in the control horn, it HAS to pass through the hinge line of the control surface. If the control horns are mounted too far from the hinge line (this is common), then the geometry is off and slack cable really does go droopy.

Here's what majortom left out: If your geometry is off and you get a droopy cable, you MAY get differential motion of the control surface. It may even be differential at low deflections with the end points coming out the same. Whether this is a problem depends on how accurately the airplane responds to what you tell it.