Unfortunately, you can't assume anything because all sitters on Rover are independent and decide on what they're going to do and for what rate.
House sitting is by far the most controversial and subject to interpretation, despite Rover's FAQ saying that each night of house sitting is good for up to 24 hours of care, just like boarding, and should therefore be considered an all-inclusive service. My view of what that entails is the same as yours, and as such should be considered a premium service commanding a higher rate because the sitter has to uproot herself/himself while providing some added security for your home.
However--and this is a big however--not everyone does share our interpretation. Some sitters will arrive in the evening and leave in the morning, e.g., 7pm-7am, and may charge for drop-ins/walks during the day. Some sitters will move in and use your home as their base of operation while performing drop-ins/walks for other animals under their care. Some sitters have full-time jobs or are students and will return periodically as permitted by their schedules to check on the pet.
So what this boils down to is that you have to ask either through Rover's messaging system or at the Meet & Greet (highly recommended) exactly how the sitter operates. You have to communicate your needs and find someone who will meet them. You don't have to accept what they'll do. You should be able to find a sitter that will do as you wish. Remember, though, the lower the rate, the lower level of service.