I'm not familiar with this particular PCB revision design, are you sure there is no any errors in PCB routing?
Ajusment can correct up 2 or even more times discrepancy, but that's not a good sign.
Normally, initial discrepancy shouldn't be more than 10-20% of actual value of the resistor. Let's go through the Setup again to make sure nothing is missing. Here is the author's web site -
https://www.rlc-esr.ru/index.php?option=com_content&view=article&id=78&Itemid=95
I'll try my best to help you.
1. Check +5v/-5v Voltages. I saw you did it already...
2. Adjustments:
2.1 Press and hold "+" button, while you power on the meter, short the leads. Meter will go Setup mode.
Ajust R4 to set minimal reading in 1 Ohm channel
(but not zero!). 0001...0003 will be enough.
While still holding "+" button, press "Set" button - it will save the settings. Note: you have to use version 1.1 (latest) of the firmware, especially if you use PIC16F876A CPU.
3. Setting up correction factors. There are 3 of them - one for 1 Ohm channel, one for 10 Ohm channel and one for capacitance.
Make sure you use precision (1% or better) inductance-free resitors 1 Ohm, 10 Ohm and capacitor, like 1000 uF with verified (trusted) value. Measure and write down their measured values.
Press and hold "Set" button while power on the meter. It will go to Coefficients correction mode.
Switching between 1 Ohm, 10 Ohms and Cx - button "Set", Saving - same button. Changing values - buttons "+" and "-".
If discrepancy is too big (like 2 times), try to replace TL431 to other maker, preferrably from well-known brands like TI, Fairchild, Motorola. Avoid PL431 - they are not working well in this meter. Check the 10ma current (should be 10 +/-0,5ma),sometimes you may have to change resistor 180 Ohms (or transistor).
Properly ajusted meter will have precision of about 1% and even better. Good luck!