When you short the voice coil, you increase damping. That makes Qts go down. When the voice coil is open, it has no effect, no change on Qts. When you partially short it, as in putting a resistor across it of a few ohms, it is in between.This is in parallel with the output impedance of the amplifier. Less impedance makes more damping, lower system Q. Higher output impedance makes less damping, higher total Q.