It is, however, an expensive method.
Or if you have garbage bags large enough to drape over the top, those will work, and then you can reuse them for garbage! I've done this before and it works pretty well.
The short answer as you guessed is YES, your fish are in danger should any of the chemicals make their way into the tank. It's important to cover the tank as the spray will get into the air at least some.
I like the garbage bag method myself because it's cheap and easy to remove once done.
That's also a worrisome time, the removal. It needs to be done in such a way as to keep any poison that landed on the plastic from getting into the tank. For this reason I normally put a layer of paper towels down over the plastic so they absorb the poison. I can then remove them first and the poison with them and then the bag.
Depending where you live you could buy cling film in £land or a dollar store (probably, not been a dollar store in years). Personally I'd go with the cling film as it is easier to seal.
I'd put some layers of clingfilm on, then a towel. Though I always have a towel over one of my tanks because it's right behind my chair and the fish scare easily. Be sure to put the towel in boiling water or a sanitize setting in the wash to get the chemicals off. I wouldn't put down the towel alone though, as the chemicals could seep through it. And if you have a bubbler, put that somewhere where it wont be exposed to the general air.
There may also be some mileage in talking to the bug control company. They may; 1, ignore you, 2, use different chemicals (although I'd still cover the tanks), 3, provide a cover or, worst option, 4, insist that you take the fish elsewhere when they treat (which would be a pain).
Well the fish are your property in a way, so as Dr. Rob says I wonder if you can talk to them in regards to that, because they can damage what you own.
Imagine someone goes into your place and puts rats poison when you have dogs and cats around.
I also think you have to be careful when covering the tanks to leave some type of air going in for oxygen exchange.
It depends on what they are going to use. Some companies use airborne chemicals, this could have serious consequences as the chemicals will be absorbed into the water of your tank in the same way as oxygen does. I would go with the clingfilm and turn off any air pump you have.
The bigger the tank the longer you can leave the film on. It would be a good idea to ask the company how long the chemicals they use will be active, this will give you a time scale.