In the times before strain gauges and electronic transducers, the forces on the wind tunnel model were measured with scales. To avoid interference as much as possible, the model was hung on strings, the scales being mounted above the measurement area of the tunnel. Since the forces in upright flight were of the highest interest, gravity plus lift would make sure that the strings were always taut. If the model were hung upright, the lift might grow bigger than the weight, and the model would move towards the scales.
Today, the orientation of the model can be either way, and only in exceptional cases there is a strong reason for placing it upside down. This might be when unusual attitudes together with the supporting sting (the long spike on which the model sits) would block one part of the wind tunnel cross section too much, or if movement restrictions of the sting force a certain orientation.
Another reason is flow visualization techniques: Sometimes it helps to put a coat of a mixture of petroleum and pigments on the surface and to watch where the pigments are blown by the flow (this is called an Anstrichbild). Obviously, it helps to place the surface of interest on top.