Other mistake: At one point during the sub-titled Russian scenes, the word Annihilation is used. However, it was mis-spelled as Anihilation.
Other mistake: When Clark cut the Ukrainian fence with a gas device, the following two shots of the fence show that the links were clearly not cut, but just undamaged cyclone fencing.
Answer: The President telling Cabot to "get the people out of here" is just a political life boat. If asked what he did when he found out about the bomb he can "honestly" say he asked for an evacuation.
It's unlikely at such a time of panic that one would consider a 'political life boat'. There's also nothing in the character as presented to suggest that would be his thought process. The president's just been told that there's a bomb in Baltimore (not the building) and says "get those people out of the stadium." He's being evacuated from a location that contains thousands of other people. It's fair to assume he knows all those people are also in danger so wants them evacuated too.