"He basically found us. He kept coming into our house. We chased him away but he kept coming back," Mr Theijssen said.
Jet's old owners relocated and asked the Theijssens if they would take the cat.
Mr Theijssen assumed Jet may have accidentally taken a ride in someone's car and ended up in a foreign neighbourhood.
Mr Theijssen said the reward was money they had saved for a holiday.
Joanne Austin, owner of Siamese cat breeders Brenner Cats, said that despite Siamese kittens selling for about $600, Jet's age meant he probably would not have been taken for his financial value.
Ms Austin described Siamese cats as having "dog-like personalities".
"Some can be taught to fetch, they're a lot more active than a lot of other cats," she said.