Surprising Inrush Current on a MOSFET Switch?
It looks like your power source is on the verge of instability. Could start oscillating anytime, and you will have a bigger problem. 

Keep in mind that the SQM40031EL has about 30 nF input capacitance, which can provide a good impulse kick (~30 ns) when the control transistor U28 turns on. As result the input has the same drop of ~1 V in both cases, with load, and without it. The rest is the reaction of PSU to the step load. 

As a matter of fact, this kind of step load test is a must for checking stability margins of power supplies.