How does Tom do this? It's not Rocket Science. He thinks in terms of mental pictures and let those images represent what he wishes to remember.
He ponders in groups of seven. To Tom that is one picture. This mental impression could be Harry Potter's blue Ford Anglia or Paddington Bear meeting the Queen. Anything you dream of. Then this illusory madness is associated with numbers. A private language only his mind can see. For instance ninety nine is an Ice Cream, seventy three is a Red London Bus and ten will always be Larry the Cat. So if the next Pi numbers were 2107399, Tom would see two Larry the Downing Street Mouser Cats on a Red London Bus fighting over an Ice Cream. This story line to collide with the next draft of his imagination. It works! It's all ludicrous pictures!