I just started on Rover and this would be my first booking, I have a day job would I need to try to get off? I don't know if I am suppose to stay at the persons house the whole entire time or if I can come and go as needed
When you housesit, it does mean that you stay at the home overnight and spend a majority of your time there. However, all details of an engagement should be discussed with the client before you accept a job. It could be that the owner doesn't have a problem with you not staying overnight or leaving during the day to run errands, etc. However, it all should be discussed beforehand. The client should be made aware that you have another job during the day and how you plan to take care of their pet.
There are alternatives to housesitting. You could provide drop-in visits, which are 30 minutes with the pet to feed, walk, play, etc.
Do a search here on the board of other important concerns and great advice about sitting at someone else's home.
I agree with this answer. All responsibilities and expectations should be discussed either in messages or at the M&G prior to making the reservation. Some clients are ok with leaving their dog alone during the day, some are not. Just make sure that you make your schedule known as soon as possible.