The history of Rusty's is unknown. It is likely that Rusty's was around when Old Man Jenkins was young. It was also likely that it suffered the same faith as Stinky's or more likely, Rusty died and it was closed down. Old Man Jenkins would not taste a Rusty on Rye again, until SpongeBob brings back Rusty Rickets from the dead in the episode "Séance Shméance."
It appeared in SpongeBob Moves In! before the American premiere date of "Séance Shméance," its official appearance.
In SpongeBob Moves In!, Rusty's Rib Eye is called "Rusty's Ribeye" with no space between the words "rib" and "eye."