Tony made it from the hospital to CTU in a matter of minutes.
Real-time violation: At the top of the hour as the jet takes off and flies for Mexico, the sun is out in full force. When we see the presidential motorcade fifteen minutes later, they are driving in the dark with their headlights on.
As Gael is being interrogated by Chappelle in Interrogation Room 820, the interior room camera shot shows that the room door is in the process of being opened from the outside. As the camera shot changes to the exterior of the interrogation room, Tony approaches the room with Michelle, he instructs the security guard who is posted outside the interrogation room to open the door, and, as he does so, the camera pans and reveals that the door is still fully closed.
Another violation of real time; It takes about 15 seconds from the time that Adam radioed security about Gael, to the time when Gael was spotted in a stairwell. It is unlikely that Gael would be found this quickly.
Since Palmer already Jack was headed to Mexico with Ramon he could've told CTU therefore they wouldn't need to waste their resources and manpower including Chase on trying to find Jack.