You might not think that Martinez has time to stand around in the Situation Room and look worried. If that's what you think, you are wrong. That's what he's doing right now! Sterling enters, and Martinez gets snappy: "Where the hell have you been, Blake?" If you want to be left alone, I'm sure there are rooms in the White House with fewer people in them. He might want to designate an official Brooding Room. Sterling wants to talk privately, so they duck into the hall. Instead of having it in what's supposed to be one of the most secure rooms in the entire country. On his way out of the room, Martinez authorizes the busses for Sophia.
Sterling's news is that he finally realized where he'd seen Thomas before. Remember that time that Thomas and Sterling shared an elevator? It was when Thomas snuck into the hospital to switch the DNA results so Simon wouldn't be identified as one of Them. I thought at the time that it was silly for Thomas to be the one doing that. And I was right, because Sterling has suddenly become a dot-connection machine, realizing why Thomas was there and that Simon is definitely an alien. And, he says, they've been monitoring Simon's phone ever since. It would be nice to assume that this is why Simon's been kept out of the loop, but I think Sterling's talking about the time he showed Thomas to Martinez on the security camera outside the cathedral. And Simon's been mysteriously ignorant since they started cracking Sophia's phone, which is well before that. Maybe Sterling realized all this when he was face-to-face with Thomas in Inostranka, but there was no sign of that at the time.
Simon has snuck into a darkened office so he can call Sophia and be angry at her for blowing up beloved monuments and killing innocent people. Sophia tells him that they used up all their fuel on that stunt, so now they're completely defenseless. She is very clear that it was all a bluff, and that they have no other weapons at the moment. As she tells him all this, we see Martinez and Sterling watching a techie decrypting the conversation. Apparently it's encrypted in some way that requires a few hours of computer-fiddling, but even the encrypted version they're listening to sounds like distorted speech. And he's in the White House for this whole conversation, so it seems like there would be easier ways to find out what he's saying. I'm sure some of Nixon's hidden microphones are in there somewhere. You could just listen to the conversation directly.