Unlike the core series games, Pursuit has an effect similar to Counter. The user sets Counter status, which it will damage the opponents who using regular attack or any physical moves against the user.
It states that it will damage the opponents, not use the move against them.
So if Charizard used Earthquake and dealt damage, then the pursuit status would return the damage.
Also in Pokémon Mystery Dungeon there are no immunities, it simply says "It has little effect." and does very little damage.