Vomitted a worm after dewormer shot

Hi guys! I'm a little concerned about Houdini. About two weeks ago I noticed a very small, rice like worm on his behind. I took him to the vet about 5 days ago (Please don't make me feel guilty for not going immediately )
Anyways. The vet did not take a sample, but gave him the dewormer shot after I described what I found. I just came home to find semi solid vomit with what appears to be a large tapeworm. Tan, thick in width and stretchy.

Why would he vomit another worm after being dewormed 5 days prior? Misdiagnosis? Is he just getting rid of the dead worms? Have not noticed any in his litter box. Thanks in advance!

It takes more than one worming to rid a cat of its infestation. Sometimes after worming, cats and kittens will throw up dead parasites. Dead is good. Follow up with your veterinarian regarding his next worming. Ask what sort of wormer it was - hopefully it does roundworms, too, because often where there's one, the other is there also.

A coworker rescued Patches from outside as an orphaned kitten so I am sure he had a heavy load of worms.  Shortly after deworming, his was multiple days of oral medicine, I saw a live worm hanging out of his mouth.  Of course I freaked out because that was really gross.  I know from my own personal experience that they can come out through the mouth as well.  The way I understand they let go of where they are latched on at inside and they can travel up through the mouth rather than the usual route.