I can only speculate, but it doesn't surprise me that a lot of workers would know that something called the Manhattan Project existed. There were massive facilities like Oak Ridge built very quickly, so that meant a lot of construction workers, welders, etc. had to be involved. They might well have heard the term "Manhattan Project" without knowing what it meant. Some $2 billion was spent in about 3 years (roughly $22 billion in today's dollars) on the Manhattan Project, so it would be hard to keep it completely secret.

As for your grandfather, the work that he and millions of other men and women did to build the weapons of war was essential to winning the war. It was often dirty and dangerous work and seldom glamorous, but there was no way we could've won without their efforts. The logistical challenges of fielding and supplying a military force of about 16 million are mind boggling. As but one example, I watched a program on the History channel over the weekend about Japanese weapons of WWII. It mentioned that the US produced more light machine guns in a single month than Japan could produce during the entire war.