Why is Eid-ul-Fitr determined to be Wednesday, June 5th? In Islam, Eid-ul-Fitr is celebrated the day after the sighting of the new moon. The Ahmadiyya Muslim Community uses the calculation of the moon to determine when the moon can possibly be visible by the naked eye. Instead of simply following Saudi Arabia, which is thousands of miles away, Muslims are to determine Eid based on when the moon is visible with the naked eye. 
The below image illustrates the different gradients of visibility of the moon on Monday, June 3rd: 
As you can see, there is no place in the U.S. that is covered in red - meaning that there is nowhere in the U.S. where there is even a possibility that the moon will be visible today with the naked eye. There isn't even any part of the U.S. that is covered in the orange color, which indicates the possibility of viewing the moon with the naked eye only in perfect conditions. So literally there is no ability for the moon to be sighted in America on Monday, June 3rd.  This means that Eid-ul-Fitr in America cannot be on Tuesday, June 4th.
The following is the map for June 4th: 

On Tuesday, June 4th, the entire country (and most of the world) is covered with red, which means that on Tuesday we will all be able to see the moon with the naked eye, InshaAllah. 

That means Eid is Wednesday, June 5th, InshaAllah.