I think it is related to the power consumption of the client device charging by the power bank. 

QIG lists some explanations of the led indicator, and for the power bank, when it has low battery, the indicator will remind us to charge itself, while it won't switch it off unless it ran out of battery. 

i was mainly interested in the function of the button...

(seems this was not clear in my asking ;-) )

i would like to know if the button can be used to switch the output on and off.

or if the button needs to be pushed to switch the output on

but the output only switches off if the client-device disconnects*1 or the powerbank itself is empty

*1 or uses less than XXmA power. for most of the powerbanks i found information on this its about ~50mA..

sunny greetings

stefan