>>132855464>>132855585There's two main ways I can think of for the reason why they have similar puppets with similar control schemes:
1. The old man makes the puppets himself. The girl takes one of them for her own use. This makes them likely to be related (father-daughter) because you don't give away your puppets to just anybody.
2. The old man and the girl bought from the same puppetmaker. There's no way "Sumire" and "Sakura" could be store-bought so they have to be specially made. This could mean there's more than just the two of them doing this stunt.
If the girl was just a bystander following his footsteps she wouldn't be able to buy a puppet just like Sumire so easily, nor have it made so closely resembling Sumire to the point the old man can easily slip in and use it the same way.