That turns out to not be the case, in my experience.
/john
Glad you were not hurt.
I have several 9mmP cases that look like little mushrooms. They were fired in a pistol chambered for 40 S&W. I was watching a fella at the local range show his wife how to shoot. His S&W pistol was acting like a single shot. He would have to cycle the slide after every shot and the bullets were hitting the target sideways. I asked him what the problem was, and he said that his gun was broken as it would not cycle properly. He asked if I could take a look at it. The pistol was clearly marked as 40 S&W, but the box of ammo he was using was clearly marked 9mm. I showed him the fired cases and what he was doing wrong.
He walked off grumbling something about letting the wife pack the ammo in his bag!!!
After a good night's sleep, I have a fresh perspective on your experience. Recall that I mentioned the .45 ACP headspaces on the case mouth. That is because it is a straight-walled case. The case mouth diameter when crimped is the same as the case head diameter. That is NOT the case with 9mm brass. The 9mm and .380 ACP are tapered. The case mouth is smaller than the case head. The consequence is that your .380 was probably dangling into the firing chamber, hanging by the case head. A proper fit between the brass cartridge case and firing chamber provides support for the brass on all surfaces. The .380 ACP in the 9mm chamber would have no support beyond the case head. Upon insertion, the weight of the bullet at the case mouth would be slightly nose down i.e. the cartridge would not be colinear with the bore of the barrel. The bolt face could exert pressure on the lower edge of the case head to straighten that misalignment. Under this condition, the firing pin would have access to the primer. Firing that round would raise the possibility of pressure ballooning of the unsupported brass casing between the case head and case mouth. A burst or split may also occur. The consequence might be a jammed piece of brass or a failed extraction. It is something you definitely want to avoid.
The .380 also has a smaller bullet weight and powder charge. Even if you successfully fire the round, the mass of the slide and recoil spring is tuned to the mass of a 9mm bullet and powder charge. It is unlikely that enough energy will be transferred to the slide to properly cycle the blow back action of the 9mm pistol.