These little servos have some variability in response from sample to sample. Since the tilt servo will have a limited range of motion, you may need to adjust either the physical orientation or the code to keep it operating within that range. The steps below should get you pretty close.
Slide the servo into the eyeball and align the shaft with the hole.
Position the motor assembly so that it is fully clockwise inside the eyeball and press the shaft into the hole.
Arrange the wires around the servo to avoid snags when turning.
Feed the wires through the slot in the eye-cup insert and align the other servo shaft with the hole.