Pro Mini 328P not running on stand alone micro usb power supply

I have a Pro Mini 328P 3.3V that has an ADXL 345 and a MicroSD Card Adapter properly hooked to it and programmed using an Arduino UNO. I have checked by only connecting the UNO's 3.3V and GND to the Pro Mini's VCC and GND respectively and the Pro Mini works fine taking readings from the ADXL 345 Accelerometer and saving them to the MicroSD card in a "accel.txt" file. But when I connect the Pro Mini to a MicroUSB power supply (pictured below), it powers up but does not record any values, neither it creates the "accel.txt" file in the MicroSD card attached. I have connected OUT+ to the Pro Mini's VCC and OUT- to the GND.

Where do I start debugging this problem from? What exactly am I doing wrong here?

What is the voltage on those OUT pins?

I would expect 5V on those.

The 328P has no problems with 5V, but your other devices could be killed or malfunction,
so that would match the symptoms you are describing.

What is that picture supposed to be showing? You cannot see where the two wires are connected on the mini. Also, I have no idea what the USB board is.

To me it looks like a LiPo charger / power bank / protection board.

Mine generates 5V on the OUT pins, you would attach the power bank output jacks to these pins.