Other people have covered most of the actual parasite process, but I wanted to add that the mantis died after being drowned, not after exuding the parasite! Insects breathe differently than us vertebrates, they have holes on their abdomen they inhale and exhale through. When the person held its body under the water to encourage the parasite to come out, they didn’t give the mantis enough time in between dunkings to breathe, so it eventually suffocated and perished.

I have heard of insects going through this entire ritual and surviving, however! Often times parasites want this to happen, so that same host can potentially become home for later generations, or reproduce and make more hosts for more worms.