Revealing mistake: In the scene where Jack Ryan uses the radio after the helicopter crash, the film is reversed - the word frequency appears as a mirror image.
Revealing mistake: In the scene where the president's motorcade is going to the stadium, it travels on overpasses, but there is other traffic passing below. These over / underpasses would have been temporarily shut down as well while the motorcade goes by.
Revealing mistake: At the end of the movie when Spinnaker is approaching Jack and Cathy, the wide shot shows the couple sitting further apart. When it jumps to the close view, she is much closer to Jack.
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.