As I understand they're happy enough staying in a small container as long as you take them out for walks. Here.

[She switches to video, and holds up a pokeball.] Professor Sycamore can explain them better, but they're for holding certain creatures you'll find out and around the city and the forest. They came from his reality.

[And at this point she drops the ball onto the floor, and out comes her ghost companion. He's around the size of a cat and seems very interested in checking around the area for food.] This is Sprig. He's one of those creatures, but they come in all sorts of shapes and sizes - one of my friends has a pony with a mane and tail made of fire.