Neutral Shift
What the question refers to is almost without doubt neutral shift.
With a 'flying' or trimming tailplane the aerodynamic neutral is not the same as mechanically neutral.
When the stab is leading edge up, the elevator tends to be trailing edge down. As the stab is moved through its range towards leading edge down, the elevator is repositioned to an aerodynamic neutral by a device known as a neutral shift mechanism so that when it is fully leading edge down, the elevators will now be slightly trailing edge up!
Here is an extract from the B737 (classic) MM which gives figures.
"Elevator neutral
position relative to stabilizer is determined by stabilizer attitude.
The range of elevator neutral shift varies with mach trim actuator
position. With the stabilizer at 3 units of trim, the elevator neutral
position is 4 degrees down from faired. As the stabilizer leading edge
moves down the elevator neutral position moves up. When the stabilizer
moves to 10 units of trim, the elevator neutral is at zero degrees, and
with the stabilizer at 14 units of trim, the elevator neutral is 2-3/4
degrees up. Elevator maximum travel with the stabilizer at zero units is
20 degrees up and 22 degrees down."
The elevator movement can be clearly seen if with hyds powered the stab is moved. As the stab is trimmed a/c nose down so the control column moves forward as the feel and centering neutral point is moved by the neutral shift mechanism.
By the way for Genghis, the 737 has tabs. they operate as servo tabs (i.e. they deflect in the opposite sense to the elevator) to assist the elevator deflection. They are always operating but are primarily to assist the pilot with pitch control in the event of a total hydraulic failure or manual reversion.
Hope this helps.