It just depends on your preference. Yes, Rover requests payment for only overnights (without respect to drop off and pick up times). But, you have the option of charging for daycare or overstays as others have mentioned above. You should ask about drop off and pick up times pretty early. If not during initial messages, then during the meet-up. If you want to be paid for someone dropping their dog off early or picking them up late, that's the time to relate that information.
That said, I don't charge extra for a dog to be dropped off early or picked up late. I get a lot of repeat business for being flexible. My go-to sitters also don't charge for "extra time," and I am a repeat client of theirs (and they sometimes "make out" a little when I don't drop my dog off until 9 PM on his first night). This may be a consequence of our circumstances. Sitting with Rover is not my primary job, I only sit on weekends, and I only sit one dog at a time. It doesn't really matter to me if the owner comes to pick their dog up at 10 PM on Sunday, I'm not sitting that night, so it's not like I missed out on anything. On the VERY rare occasion that there is some reason I have overlapping bookings (not that long ago, I took a "staycation" and made myself available for an entire week...a regular client booked for the weekend and a new client for the week), I just tell the clients that if they drop their dog off early or pick them up late, there will be another dog around for a few hours, and give them the chance to either accept or reject that arrangement. In that case, both the clients said "that's fine...thank you for being flexible." It was no skin off my back to have 3 dogs (including mine) for 4 hours.