Recently got one of those, and I was wondering what the output voltage was. I know the input is 5V, but the very-much-standart Li-ion 18650 battery I use is 3.7V I'm planning to connect a Digispark ATTINY85 board to the output, which requires also 5V. Will the ATTINY85 work properly? I heard somewhere that the output of TP4056 is 4.2V at max, but couldn't confirm that. I also have one of those booster modules (3.7->5V) (second pic). Should I use this and how?
You could always try it directly from the charger board, the processor may well run at 3.3V, using a LDO 3.3V regulator on board - and Li-Ion will feed that fine.
Failing that, connected the output from the TP4056 to the input of your booster module, which will give you 5V out.
The only issue if it the processor is running at 3.3V, as you're wasting energy boosting it to 5V, then wasting it again dropping it back down to 3.3V.