You don't set the power supply to constant current. You set a maximum current and voltage. If will limit either voltage (constant voltage) or current (constant current) to remain within these limits. Say you set the supply to 30 V, 1A. To supply 1 A to a 1 kOhm resistor would require 1 kV, so the supply limits the voltage to 30 V, which results in a current of much less than 1 A. If you now replace the resistor by a 1 Ohm resistor, 30 A would flow if the voltage were 30 V, so the supply limits the current to 1 A, resulting in a much lower voltage than 30 V.