Booked before accepting, normal?

It is likely that they were new to Rover, and so were unsure about the booking process. Perhaps they had an emergency, were in a time crunch, or had someone cancel on them and were looking for last minute help. It is not unusual to receive requests from clients who had just joined the same day, and sometimes they haven't filled out all of the information prior to sending a request. This is something I usually discuss at Meet & Greet. I probably wouldn't have accepted the request either, because I'm not comfortable making a visit without meeting the client and especially the dogs beforehand to get acquainted. I wouldn't be too fearful or anxious about people who have joined the same day, as if you limit yourself to only those that have used Rover in the past, it may be because they keep having to change sitters due to something unpleasant (aggressive dog, extremely nit-picky owner, etc.)