Vinca (periwinkle) are susceptible to nematodes and fungus. I have heard if you have a problem with them do not replant new ones in the same place. Because they are a tender perennial, I have mine from last year, you should periodically move them and plant something else where they were. I understand these were new for you. I would think fungus is your problem. Whether the fungus was in the plants to begin with or in your soil it would stand to reason the fungus is now in the soil. Sometimes baking soda washes or hydrogen peroxide washes can help the soil or you could try a fungicide. Sorry I do not have any recommendations on fungicides.
