I have read in various places including ICU/CZ posts clearly stating that one should not mix Antibiotics . Stop one before starting another.
As to your dog, the positive response to an Antibiotic indicates a bacterial infection, not a worm invasion.
Death to and/or sterility of worms through tetracycline therapy would not be immediate.
From Wiki "Wolbachia": "Wolbachia is a genus of bacteria which infects arthropod species, including a high proportion of insects, as well as some nematodes....Wolbachia infects a variety of isopod species, spiders, mites, and many species of filarial nematodes (a type of parasitic worm), including those causing onchocerciasis ("River Blindness") and elephantiasis in humans as well as heartworms in dogs."