Because the bond between Pokemon and Trainer is so strong in Minami, the Pokemon is always with the trainer. Also note that Pokeballs are extremely frowned upon. Of course, if you happened to bond with a Snorlax, you're obviously not going to fit him into your dorm with you, and then the use of a Pokeball is allowed.
However, if your Pokemon is a fairly normal size, it will always be with you.
And if you have one (like a Ponyta) that doesn't go up stairs easilly, Pokeballs can also be used sparingly. However, only Trainers with such Pokemon are even issued Pokeballs, so if you're like my character with an Espeon, they don't even have a Pokeball.