If the device is designed to be charged via USB cable it usually accepts 5 V via that cable from whatever source. The charging of the internal battery is determined by the charging electronics within the device. Therefor if the charging electronics has been designed correctly there shall be no harm to the battery.
Some devices accept higher voltages or higher currents than standard USB (5 V, 500 mA) for turbocharging the device. Typically this is indicated by some sort of resistor coding of the USB port or via a protocol. If your device is designed for standard USB (5 V), it can (and very probably will) be damaged if you apply more than 5 V. If you restrict the charging voltage to 5 V, however, no harm should be done.
The specs for the hub you cite are rubbish. It is not your fault, I looked up this hub
here and it states a current of 150 mAh which is nonsense. Let us assume they mean 150 mA. This means that your 2000 mAh battery will take more than 14 hours to charge.
From a standard USB port (500 mA) charging will take more than 4 hours.