The voltage cannot remain constant. It will vary with load. The amount if will vary will be, basically, the amount it would have varied without a regulator divided by the regulator's loop gain.
If a voltage would drop 1 Volt if unregulated, a regulator circuit with a loop gain of 100 will reduce that variation to 10 mV.
So maybe the readings you get are endemic to the particular equipment you have. Read the specifications and see if it's within the parameters.
It's rare that a power supply would be regulated to much less than 0.5% but each design is different. That would correspond to 60 mV change at 12 Volts.
Additionally, if your current limit is set too closely to the actual current, it may be holding the voltage down to maintain the limit.