The problem with starting with the generator is that you won't really know what you need until you're coding the game itself. You'll need a good guess to avoid having to redo a big part of the generator once you start to see any possible problems in it when coding the game.
The opposite approach also have a downside, as you'll need to create one or two maps by hand, what isn't that much of a problem, but your game will have just these test cases and you can then have some nasty bugs that for a random reason don't appear on your hand-made maps.
Another possible approach is to code the generator and the game "simultaneously". Whenever you add a given feature to the game that affects your levels you add support for it to your generator. This is a safer approach, but it will probably take some rework now and then; you'll do a little rework to guarantee you won't do a lot of it. Now, if by generator you mean editor you'll need to create new maps whenever you make significant changes to your level system. If you really mean generator (as in a procedural generator) this wouldn't be a problem at all.