Testing 5V USB battery pack
Most commonly used electronics for 5V USB battery packs are quite similar.

Of course inside there is a charger that uses 5V input to charge the batteries with constant current. Charging stops when batteries reach 4.15.-4.25V depending on model.

Also there is a boost regultator which boosts battery voltage (2.5V to 4.25V) to 5V on USB output plug. Discharging also is controlled and stops at a certain voltage but is this voltage (3.00, 2.75, 2.50) correctly matched with battery specs one can only hope if the bank is "no name" brand.

I doubt you can measure this correct with a device like SkyRC S60 that is designed to work with raw battery cells.

Measuring voltage - most of these battery banks even being cheap have something "smart" in them. When there is no load attached (when load current is neglectably small) average output voltage is less than 5V and output LED is turned off. This is done to minimize self discharge of the system. So measuring 4.5V may be normal in this state and it doesn't mean weak battery.

How to measure bank's capacity? Charge up the bank for long enough period - like 24h, then connect a constant load and measure how much time it will take to turn off. You can connect a 10ohm/5W resistor for 0.5A load current and start waiting. If the pack is really 10'000mAh time would be about 14-15h. You can try with smaller ressitor (for example 4x10ohm/5W in parallel) to discharge with 2A on the USB but this may be too much for the bank's electronics and even if it handles this current, it will discharge your cells faster and you will get wrong reading. 

I think the battery bank will lower its output voltage only on current overload, but not when its cells are empty. On discharged cells the bank would stop and its output will be 0.