I have always found that the most submissive cow gets to be babysitter of a large group or cows that calve relatively at the same time take turns who gets to babysit the young ones.
I believe the instinct comes from both parents, but if their dam was a loving, nurturing mother, than the calf most likely will pick up on that and do the same with their calves .
Stormy and Magic's dam tried to kill them both when they were born, so I raised them and now they both are two of the best mothers in the herd. They always know where their calves are and will babysit other calves as well.