I used to work in pest control for roughly 4 years. When you say "fumigate", do you actually mean putting a tent over the house and releasing a pesticide gas into the air? Or, perhaps closing off a room and releasing a pesticide gas just in that room? Or, do you simply mean someone is going to come in and spray around your home with a liquid along baseboards, and around the foundation outside? For that matter, what are you trying to kill? Perhaps I might offer some insight.
If you are talking about spraying a liquid along baseboards and outside, then your tank should be fine if the chemical is applied properly.
If you are talking about a gas being released in the room, then I think you may have problems. Somehow you would have to seal off your tank such that no pesticide containing air could get into your tank. As you can imagine, not an easy task.