The Pokémon encountered cannot be the Pokémon rescued from the thugs at the Opal Ward.
Plants aren't usually so fond of fall...
During clear or sunny days, a Budew is precariously walking on the wall near the gate to the desert. If you have a PokeSnax, the Budew will catch the scent and leap off to join you.
This article contains plot details about events that occur later in the game.
To the left of the wall is the location of the thief who stole your Pokémon purchased at the Grand Hall. Upon confronting him, he demands 500 before giving it back. Paying this amount results in him revealing that he and the fisherman that sold the Pokémon actually worked together to scam unsuspecting trainers, and dare you to defeat them to retrieve your purchase.
...But after beating them, the street rat admits that a kid stole it from him on his way home, and he can't give it back. The search continues...
This event is initiated by speaking to the woman inside the house by the fountain and listening to her fear over kidnappings. After this, enter the formerly-empty house next to Hotshot Roger, where you will find two suspicious people discussing plans for liberating a Pokémon, who flee upon discovering the player eavesdropping. Return to the woman's house, where the duo is attempting to take the woman's Igglybuff. When you interrupt them, they recite an anthem detailing their motives and attack.