For now, Genie+ is strictly next available.
So let's say you get a TOT for 10:10, as per your example. You want to ride Big Thunder Mountain in the afternoon. If, at 10:10 am, the next available BTMRR is 2:20, you can book it immediately. If the next available BTMRR is 11:10 am, you'd have to wait a while, book more DHS stuff up to then.
I suspect that in most cases, the next available will be within 1-2 hours. So if I'm right (we will need to wait and see), then you wouldn't really think about booking rides for 2:00 pm until after noon.