Preferably, I'd put enemies and moving objects in their starting positions if possible. Although personally, I like to snap such sprites to the background grid horizontally, meaning that if a sprites is 16 pixels wide for example, I'll try to position it so that it's aligned with the tiles of the stage, even if on the first frame you see it, it's actually one or two pixels off that mark.
It's a bit tedious, but it just looks cleaner to me. But it does make me prefer to leave at least minor enemies off my maps if possible.
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Current project: Castlevania: Aria Of Sorrow (GBA)
Upcoming project: Castlevania Legends (GB)