No, the two to three hours is just a suggestion. The host may have to go to work the next day but may want to meet again. Or they may have taken the day off to host and relax so it depends on the host. You will be able to communicate with the host directly once your booking has been completed so these details can be clarified then and of course on the day of the actual visit. Oftentimes hosts may offer to meet a little earlier to show you around the neighborhood or visit a supermarket together.
If you have to be somewhere at a certain time after the Nagomi Visit make sure to share that information with your host before the visit.