Lots of good advise so far and I also agree with most of it. My experience is as your soil gets better and looser with more organic matter the potato harvest will be better. As the straw you mulched with rots that will help your soil so all is not lost. I plant mine just under the soil so I don’t have to dig so far down (you can plant them deeper). As others have said they do spread outward though that depends on the variety, some stay by the mother spud, some travel. I mulch them well with hay (my preference since it has more nutrients than straw), maybe 6", enough to cover well. But many mulch materials will work. When the plants are growing well I put on more hay, snugging it up under the plants against the stems. Some folks do with this dirt not mulch. It does the same thing, gives the new potatoes a place to grow easily and keeps them out of the sun.
It helps to check them later in the season to make sure all tubers are well covered with dirt or mulch. I find the mature plant stems tend to fall outward, leaving the center open and tubers exposed. Sun greened tubers are throw-aways which is always irritating when I’ve let that happen.
I’ve also seen many articles over the years about growing potatoes in bins of some sort so I can understand your confusion! But as fruitnut said, the tops do need the sun but the tubers definitely want to stay covered. There are a lot of different ways to do that, successfully. But one learns with experience (and the learning never ends!). I’ve no doubt you’ll be growing some good spuds in future years.