No, Rover doesn't automatically adjust a billing if the boarding period goes over the 24-hour period. Rover has no idea when a dog is dropped off and picked up. Moreover, there are many sitters who have their own rules about the boarding period (i.e., specified dropoff and pickup time windows). The lack of uniformity would render any system useless. Because all Rover sitters are independent contractors, they can set whatever rules they like so long as they communicate with potential owners what they'll be getting.
It is up to Rover sitters to find out before the booking is confirmed and paid what the dropoff and pickup times are so that ihe invoice can be modified to ensure its accuracy. I make sure first-time customers understand that each "night" of billing is good for up to 24 hours of care and that there will be additional charges if it goes over, just as would occur at a boarding facility. I do give them a couple of hours leeway, but don't tell them that, otherwise, I would have more pushing the envelope. If they drop a dog off in the morning and pick it up in the evening, I will charge for another full day since it will be over 10 hours. Not a single customer has ever balked when I have explained.
Yes, it would be easier if Rover's system had a built-in capability, but I wouldn't hold my breath.
Between me and the pet owner, we would agree if it will not take more than half a day to return it's fine as is. If they need more than half a day. They request one more day. Each sitter is different though. I give a day for free if they hit car troubles and stuff like that though. This is me though