2.5" drives typically use a 5v at 500mA source, some even need two USB plugs connected to provide enough current.
Using 6v on a 5v device shouldn't be a massive problem but with these types of adapters you get a much higher voltage at low and no load times. So your 6v might be measuring as much as 12v as you connect it. 12v on a 5v device is not a good thing.
What you need is a proper regulated power supply that will output 6v no matter what the load.
I probably wouldn't use this adapter to be honest.
Get a Mains to USB adapter thingy, that'll be better for your device.