A square wave with other than 50% duty cycle comtains a DC part. For the RMS readings there is sometime a confusion in showing only the AC part or the combined AC and DC value. So both readings can be correct just different things. 1 V für AC +DC and 0.6 V for the AC coupled part. For DMMs it is normal to show the AC coupled RMS, so without the DC.
A "square wave" with other than a 50% duy cycle is no longer a square wave ------- It is a rectangular wave.
ln any case, "duty cycle" is not an appropriate term for a rectangular waveform which is bipolar.
Duty cycle applies to rectangular waves which return to zero volts for some proportion of each cycle.
("unipolar")
A bipolar rectangular wave is able to produce power for the whole cycle if applied to a resistive load, a unipolar rectangular wave cannot.
In each case, the waveform's RMS voltage is the equivalent DC voltage which would be necessary to dissipate the same power in a resistive load.
A RMS meter which cannot distnguish between unipolar & bipolar waveforms will get at least one of them wrong.