Almost always there are two reasons the potatoes turned black...  exposure to air or oxygen and black spot bruising. As soon as the potatoes are cut I would try to get them into some sort of water and acid mixture, usually a gallon of water needs 1 tablespoon of concentrated lemon juice or white wine vinegar. Here are a few Dr. Potato blogs that will help explain this:

• How Long Can Peeled Idaho® Potatoes Sit in Water?
• Potatoes Turning Black After Being Cooked and Peeled in a Commercial Peeler
• Oxidizing potatoes

The bruising comes from storing the potatoes too cold. A pressure bruise will show up underneath the skin but the blackening may not appear until the potato is boiled or cooked in some manner. Here is a link explaining:

• It's Natural to Have Potato Bruising