The President of Earth, is automatically the president of the federation council. And the rest of the federation membership can just suck on that.
Earth Rules !!!!!
Seriously, there are a few possibilities.
The federation president didn't
have the power to legally declare a state of emergency, even on Earth, but he legally could give the admiral and Sisko a provisional go ahead with their side of a SOE, get the ball rolling. The fed prez then would have to legally call the Earth leader and government to make the SOE official. But he knew (or presumed) that they would agree with him once he presented the evidence.
The admiral and Sisko went to the fed prez, instead of going directly to the Earth government, because they were going through their chain of command.
If the Earth government didn't agree to the SOE (which apparently they did), then the fed prez would have had to reverse his instructions to the admiral and Sisko.
Or, the federation presidents have special powers when it comes to Earth, owing to the council being located there, Earth being the center of the federation in many ways. He could only declare a state of emergency here and no where else in the federation.