No, programs don’t typically expand to fill all available memory. They use however much they need, almost regardless of how much you actually have, and therein lies the source of most memory-related slowdowns.
There are lots of reasons one might want multiple gigabytes of memory, but it shouldn’t really be for something as simple as FireFox. I’d have to agree that someone’s a memory hog in that situation, but it might not be FireFox itself.
Your situation – everything just working with relatively low memory usage – is actually much more common.