Papi couldn't bring himself to sell or melt down the automaton so he gave it to a museum but obviously it didn't work because he took out parts to make his camera. Hugo's Dad, working at the museum, saw this automaton sitting there going to waste so he took ithome to fix with his son, Hugo. The automaton, made by Papi, had a pre-programmed picture of the rocket in the moon's eye signed by Papi, his most famous film.
Hug's Dad happened to see that film by Papi as his first film as a coincidence, he was about the right age to be a kid when Papi was making the films (i think the film actually went a bit out of its way when Hugo asked Isabelle about his 'granddad'.
Anyway, there is no direct connection between Papi and Hugo's Dad, just a bit of poetic coincidence that a story like this needs to have.