Unlike the general misconception, Jammu is as safe as any other city in India. Only Kashmir is inflicted by riots and has a conflict environment. My sister had no doubts when she made the decision to pursue MBA from IIM Jammu. In fact, even our parents did not worry about her relentlessly. 

As a part, a little concern on their part is justified. But if the riots and conflicts are the reason your parents can rest assured as Jammu is a very safe city.

Moreover, IITs and IIMs are institutes of great national importance. Hence strict regulations are imposed to maintain safety within the campus.