The upper one kilometer of the tropical and subtropical oceans is occupied by relatively warm and salty water with the cold and fresh water beneath. This is the case of positive vertical gradient of salinity and temperature. However, the density gradient is negative. The physical mechanism is shown in the figure. A parcel of fluid displaced downwards gains thermal equilibrium with its surrounding while remaining salty. Thus this fluid parcel would be less buoyant than its surrounding and continues to fall under the gravity leading to salt finger propagating downward.
Figure: Double diffusive instability forming salt fingers in water.
Source: J. S. Turner in Double Diffusive Convection, edited by A Brandt an H.J. Fernando, 1995. Figure: Physical Mechanism of salt fingering.
source: https://gfd.whoi.edu/wp-content/uploads/sites/18/2018/03/lecture10_136335.pdf
Watch a video showing salt fingers.