Cat Worms and Cat Health Issues

I Just Used Milbemax To De-worm My 5 Month Old Kitten?

Is one treatment really enough? Worms have cycles so how do you know that the eggs are killed too? I got it through the vet so they should know what they are talking about. I was told that if I was worried about this that I could do it again in 2 months. He is an indoor cat so won’t be getting re-infected from eating mice but I swear he must have had worms since I adopted him although I was told that he was treated with a de-wormer. It was just by chance that I saw one in his stool (SCREAM). Also after I gave it to him he threw up although I don’t know how long after, but how do I know it was long enough for the pill to work? His throw up was a mix of his food and peaces of tape worms (OMG). He has thrown up in the past but I have never seen worms in it. Does this mean it was working? Normally I would just call his vet, but it’s the weekend. Can anyone help?
I love my little guy and want him to be healthy!
Thank you!! =)