Given a benchtop power supply, you can turn the voltage up and then down, and it goes down. Most have a substantial amount of output capacitance, and can be driving an external cap too. So something pulls the output down.
I guess that there are no standards for this, but I've never seen a supply that just hangs high when it's cranked down.
I'm designing some programmable multi-channel power suplies and that is one of many tangled issues in the project.