It never really states why but here's what happened in my opinion :
Palkia seemes quite Territorial because when Dialga "invades" Palkia's territory he launches out on a full scale attack
The two fight until Palkia is injured by Dialga and goes into the Human World.
Dialga follows after it and they fight on Earth.
Throughout the entire Movie Darkrai is mistakened for being Evil but he's actually a "Good Guy". He saved Alicia from falling down a cliff and wasn't actually meant to cause any harm. Remember he sacrifices himself and took a Spacial Rend and roar of Time from both sides. Suggesting that he's pretty strong and as well as not wanting humanity to be destroyed.
Arceus wasn't actually planning for that incident to happen and it just occurred and Darkrai being Good Natured sacrificed himself