Cupping can be a problem. It's more a matter of the characteristics of the board. Boards can twist and bow, too. It's up to the installer to be selective, choosing the best face, cutting the warp out of some pieces while discarding boards that shouldn't be used. Just because a board is in the pile, doesn't mean you have to use it on the floor, if it looks unsuitable. Expect some waste, how much will depend on the quality of the load, grading as well as the moisture content. If edges don't fit tightly, you aren't going to bend a 1x12". Being a builder from the Pine Tree State, I've done a lot with white pine. I have a written waiver that customers have to sign regarding shrinkage. Pretty much says I can't be held responsible for inevitable shrinkage, worse with the width of the boards. I put it in writing because people don't hear what you say, and they will be calling about cracks later on.
Were your other floors 12" and were they face nailed with the cut nails? Did you have the floors sanded? Cut nails are much harder than ordinary nails. They have a black coating. If the heads aren't countersunk and contact the sander, paper can get ripped and the heads of the nails brightened. Plugging can be a ton of work depending on the size of the room. Taking up that type of installation is a nightmare. Plugs can fall out and it seems like a bit much for a soft floor like pine, that will be somewhat rustic with age.
I would get a couple larger fans. You have to take a random board from the pile and cut it to expose the center, which is where you take moisture readings. Make sure to take a reading at the start for comparison. Keep acclimating until you continuously get the lowest reading, then cross your fingers.