Hi, I am a liscensed veterinary technician, so I know a little about this topic. I don't want you to take this as a the answer, IT IS ONLY MY OPINION, but it is one based on a lot of experience with the product that you have mentioned. The active ingredient in Advantage is Imidacloprid, this is a pesticide. It will kill arthropods, and if you put it in your animals mouths it may make them sick, if you don't wash your hands and handle your amphibians there is a very good chance they could also be ill. This chemical works by attacking the fleas nervous system, it is transmitted on the oils on you pets body, so it does spread in your immediate environement. If this is a significant concern to you I would consult with your veterinarian about a product called Frontline (another type of flea control) or Program.
All that being said, I personally use Advantage around my home, on my cats, and they actually are squatting over the top of my Salamandra salamandra enclosures on occasion. I have had no noticable ill effects and have not noticed any signs of toxicity in my salamanders. On a side note, you definitely do want to do something to treat the fleas on your dog (which it sounds like you are being very proactive about), and I would say that you are very safe with a product like Advantage, their are many worse options for your salamanders (flea bombs, etc)