Can you name an example of ANY power bank that spec's the minimum current before it shuts off?
I do not think I have ever seen that specified.
Apparently it usually works based on peak current, rather than average; a common technique I've seen is pulsing the dummy load every few minutes, for like a few milliseconds at a time. This is an issue that lots of people have wrestled with and there's a lot written on it. A bit of time with google will find info on what other people do about this.
Also 16mAh is not an amount of current. Current is measured in mA. Capacity of a battery is measured in mAh (milliamp hours, ie, a "100mAh" battery could supply a 10mA load for 10 hours, or a 100mA load for 1 hour).