Hey no worries, just doing an investigation.
I too don’t really remember the Arceus DW event, even tho it’s one of the first few I finally got to legitimately obtain so I should have remembered. I think it went a little bit like this: you’ve had to key in a password into Pokemon Global Link, then Game Sync (send a Mon into Dream World), and when it comes back, it’ll bring the Arceus into Entree Forest. Go to the furthest clearing, and interact with the 2D model, and it’ll initiate a “battle”. In reality you just needed to throw a poke ball, any poke ball (it wasn’t limited to Dream Ball).
It ignoring how your triggered the even for now, but if you really had a Gen 4 Arceus, it could very well be stuck in your Gen 4 or Gen 5 games; not every Arceus could go into Bank, if I’m not mistaken.