House-sitting, like boarding, is a 24-hour period of care. That includes feeding, walking, playing, giving meds, and whatever else you've agreed to do for the owner's home (taking in the mail, watering plants, etc.). It does not mean that you are tied to the home, especially if you are also walking other dogs or doing drop-ins. But the owner should be apprised of the fact that you have other clients but will spend a majority of your time in their home, especially in the evening hours. For this reason, house-sitting should be considered a premium service with a higher "nightly" charge. You are not only uprooting yourself and moving into someone else's home but more importantly providing petcare and watching their home as an added level of security.
Of course, every sitter here on Rover is independent and can set their own rules. From reading this question and the answers for quite sometime, I can say there are many interpretations. However you choose to proceed, just be sure the client knows what they're getting. Communicate what your house-sitting service includes and what it doesn't include. Many clients won't have a problem with you coming and going, so long as they feel you are devoting adequate care to their pet, which is the reason you were hired.