I have only grown sweet taters one time, and am growing some this summer after finally locating some starts at a hardware/farm supply. So I am no expert in any way. Rookie all the way.
I think you are doing okay here from the sound iof it. The vines will spread alot much like cukes or melon vines do. The potato will grow in the hill where you planted it. Since you hilled up around the start, they will be fine. I would wait about eight weeks or more (from planting date, that is.) and go back to the hill where you planted some, loosen the dirt, and feel for the potatoes, if they look about like how you imagine mature taters go ahead and dig. If they are fulll size, they will probably have already pushed the soil out of the original mound some because of the displacement. If you wish to let em go longer, cover them back up.
I found very llittle info by Googling "sweet potatoes" when I got my sweet potato starts, so am winging it myself. Advice to you is keep them watered and healthy give em time, and check em if your're curious. Don't think you can hurt em. Try looking for a garden forum or website using a different keyword. Say, like home gardening, or root crops etc. Post again please, I am interested in your results and want to help you and learn from you also. Good luck....Margo