This is a common problem with electronic loads. They have regulation loops internally to constantly monitor and adjust the load to match what you set it for.
For doing any sort of stability analysis on power supplies it is best to use simple power resistors as loads. You can build yourself a chain of 1 Ohm power resistors that you can tap off at various points to get various kinds of load.
Then to do stability testing get a MOSFET and drive it using a signal generator. Use this power transistor to switch in a extra resistor as load, letting you get a step response of your power supply under test. If you want to see it as a freqency plot, that step response can be run trough differentiation then FFT.