You make it a bit hard because I am not sure what the "medicated" is in the medicated feed you are talking about. I don't know what vaccination you are talking about. I'll try anyway.
If the vaccination you are referring to is for coccidiosis, you are correct. They should not have medicated feed if the "medicated" in the feed is either an amprolium product or an antibiotic. If it is something else, I don't know. If the vaccination is for Marek's, medicated feed does not matter. If the vaccination is for anything other than Marek's or Cocci, I don't know.
If the medicated in the medicated feed is Amprolium, Amprol, or and Amprolium product, it is not an antibiotic. It is a substance that reduces the reproduction in the chickens intestines of the protazoa that causes cocci. It does not kill the protazoa nor completely stop the protazoa from reproducing. It inhibits the protazoa from uncontrolled reproduction. Cocci is not a problem for chickens unless the number of protazoa gets out of hand.
Young chicks can develop an immunity to the protazoa that causes cocci much easier than older chicks. They need to be exposed to cocci at a very young age and allowed to develop that immunity.
There are different strains of the protazoa that causes Cocci. Immunity to one does not give immunity to all. Most problems with Cocci can be managed by keeping the brooder fairly dry. Some strains are more potent and require medication, but a dry brooder usually is enough.
The life cycle of the protazoa is that it reproduces in the chickens intestine but it can also reproduce in wet manure. The usual reason the number gets out of hand is that it reproduces a lot in the wet manure and the chick eats the wet manure.