Rover's FAQ states that house sitting means a sitter stays in your home, although they may come and go to walk other dogs, etc., They should be spending the majority of their time in your home, especially during the night.
However, this is NOT uniformly done by all Rover sitters. Some only provide an overnight service, arriving at, say, 7 pm and leaving at 7 am, and charging additional for walks/visits during the subsequent day. There are some sitters who offer a house sitting service and do not stay overnight at your home at all.
So your only recourse is to read their profiles carefully to see if they discuss how they provide the service, Once you've found someone make sure they fully understand your expectations for not only pet care but the use of your home. I don't know where you are located but the kind of house sitting you describe should be viewed as a Premium type service . You shouldn't expect anyone to uproot themselves and become exclusive to your pet for $25 night. Good luck!