The [datasheet][1] in section 8.3.11 PWM (UVLO and Enable) says

Because the PWM pin is also UVLO (undervoltage lockout and device enable), when pulled low it is necessary to ensure the output is 100% OFF. The high-side FET driver has a small leakage path to the output. Although very small (<<100 μ A), theLEDs could glow if the current was not eliminated. The 100- μ A (typical) pulldown is activated and held ON while PWM is low and ensures no light output

so disable the driver when you want to turn it off by pulling the PWM pin low from your micro. [1]: http://www.ti.com/lit/ds/symlink/tps92515hv.pdf

The datasheet in section 8.3.11 PWM (UVLO and Enable) says

Because the PWM pin is also UVLO (undervoltage lockout and device enable), when pulled low it is necessary to ensure the output is 100% OFF. The high-side FET driver has a small leakage path to the output. Although very small (<<100 μ A), theLEDs could glow if the current was not eliminated. The 100- μ A (typical) pulldown is activated and held ON while PWM is low and ensures no light output

so disable the driver when you want to turn it off by pulling the PWM pin low from your micro.