Drontal has been around for years now, some wormers will cause a dog to be sick or have the runs for a few days quite normal.
Advocate is made by Bayer which is the same as Drontal, Advocate is a monthly spot on that covers fleas,heartworm,roundworm,hookworm,whipworm. So why would your vet want to worm on top of advocate is a little odd, I could understand giving a tablet for tapeworm as that is not covered with Advocate.
I f your puppy had no probelms with Advocate than just stick to that every month & leave the Drontal
Shine