Some use the reference to drive transistors ( or FETs) switched inside the unit, and below the minimum level they do not turn fully on ( or off) enough to operate properly, giving rise to either a varying offset voltage and spurious outputs. To use a DAC with low voltage you need one with either a 4 quadrant reference input or one designed to be used as a variable attenuator.
Otherwise use a level above the minimum and divide the output down to the desired level using a buffer opamp and a resistive divider, or a fractional gain opamp circuit.