I am not sure where you live but rats are very common in rural areas anywhere in the world.
Yes, we do have rats on the island. This island in spite of all its buildings is rural and so, of course, we have rats.
Was the rat in the house?
If so, was a trap set and was it caught?
did the villa have any maintenance staff?
I am not sure who you rented from..Jennifer's Villas or gobeach?
I would assume that Annemarie from gobeach villa rentals will respond to you, if you rented through her.
I do have to agree with John though..
If you stayed there for a week and used the facilities, they would be due their rent IMHO.