The result of these quests are focus items that cause better pets to be summoned. These particular focus items are specific to just those pets that you get when you are level 50 or below. These focus items do not affect level 51+ pets, as those have different focus items.
The Shovel of Ponz improves the earth pets.
The torch of Alna improves the fire pets.
The Broom of Trilon improves the air pets.
The Stein of Ulissa improves the water pets.
One more time, these only affect pets that you get at level 49 and lower. These do not affect the "monster summoning" pets.