It is quite common that the current limit is not really fast. So it may not fully protect sensitive circuits. The problem is that some circuits take quite some current spikes and really fast engaging current limit can than also be confusing, as it could trip way before the average current reachse the limit.
The shown example with some 500 µs delivering some 10 A shows quite a bit of charge before the CC mode kicks in. This is some 5 mC, which would be some 1500 µF charged to 3 V.
Besides the actual input capacitance there is usually also some delay in the electronics that can also add to the real capacitor.
One could check this when using an even smaller voltage like 1 or 1.5 V - if the current spike gets considerably smaller it is likely a real capacitor. The electronic part often does not change much. The shape of the current spike suggests this is more like an electronics delay.
It may be an unplesant surprise, but likely not a defect, more like a not so great design. Of cause this depends on the power rating of the supply - for a 20 A supply this may be OK.