I'm not an expert on this subject but, I guess I would start by saying that all bottles are probably different. Most modern perfume bottles with stopper tops have a plastic sheath over the "plug" end of the top to ensure an air-tight fit in the bottle. I think these started showing up around 10 yrs ago. Most other stopper tops are all glass and some are ground for a tight fit and others are smooth, unground glass (not good). Ground glass stoppers are proported to be air tight as long as the fit of the stopper in the neck of the bottle is snug and it doesn't jiggle or move around when you touch it. This is the way good decanters have been made for generations. If the stopper and the the area of the bottle neck where it fits does not look frosted (white in color) then you don't have a ground glass arrangement. Smooth glass on smooth glass won't cut it. The surfaces have to be ground and the fit absolutely snug or you have no hopes for an air-tight seal.
I have heard it said by other BNrs that even the best ground glass stoppers can't be relied on to make an air tight seal, wet or dry. That may be true, but I know that stopper bottles of these sorts were also used in the farmaceutical and laboratory industries for over a hundred years.
In the end, you'll probably just have to test each bottle you intent to use to see if it has a tight seal. You can use very small, decorative bottles for display purposes and can keep the rest of the perfume in more reliable refill bottles in the cupboard. But if the fit of the stopper seems tight I don't think you have much to worry about.