I had to use a flea bomb (well, several) in my old apartment because our dog got them (learned my lesson about living in apartments). I just duct taped plastic over all the tanks for the night. Any opening that would let in air was taped up. I had no issues. I would highly suggest arranging a set time for them to spray yours. Preferrably early in the morning so that by afternoon after everything has aired out, you can go ahead and remove the plastic. I'm sure they'd be willing to work with you, especially if you are really nice about it.
"What, exactly, is the internet? Basically it is a global network exchanging digitized data in such a way that any computer, anywhere, that is equipped with a device called a 'modem', can make a noise like a duck choking on a kazoo." - Dave Barry