Will fleas jump off a dog after flea drops are applied?

Yes. They jump off and into the carpet, etc. furniture. One way to eliminate fleas on the dog is to bathe them, neck down, then do the head. You may see the fleas going down onto the nose or into the ears.

I use Eucalyptus soap, but as long as you use soap and water it will drown the fleas. Vacuum a lot, and dispose of the bag immediately to the trash. Soap works faster and more safely than pesticides with fleas. Be sure to lather up the dog or cat and don't hurry to rinse off... let the fleas absorb into the lather, then rinse.

Shampooing will eliminate the live fleas, pesticide will not; it weakens them (and your dog).