The sensitivity factor has a tolerance of +/-1 so the worse case measurement resolution will be 253*(5V/1023) = 1.237V or +/- 0.619V
So if you read 4.8V then the input could actually be anywhere between 4.18V and 5.42V
You only notice this error at the smaller input voltages because it is a larger percentage of the voltage you are trying to measure.
So the resolution is not 0.1V as you require and is not possible to do with this module, 10 bit ADC and the software you have.
You may be able to obtain a higher measurement resolution with a ADC with more bits and different software but that is yet unknown