This site has not yet been updated to reflect the changes in Reborn v19.5. It still only reflects the state of the game as of v19.16.
If the Pokémon is not holding an item, it will fetch the Poké Ball from the first failed throw of the battle.
There are no Pokémon with this ability. (It's probably a Gen 8 ability that's snuck its way into the database by mistake.)