Right at the start of the battle when the screen fades to black. With the Lua script you can see exactly when it happens. Note that it takes a couple frames to get the full spread so advance it a couple more frames after you see the Nature/PID change to get the true IVs.
Yeah you'll probably have to reset. I doubt the save states are compatible. If you already advanced the states enough you can use Enciclopedia Pokemon, which is kinda like Pokegen for 3rd gen games. You'll have to do in-game saves for that though so make sure you have a save state before you encounter the pokemon obviously.