I know the U.S. tends to do everything possible to remove dependants from areas when threats rise.
Usualy it is a warning from the state department, then it is restricted period.
Then they send in ships and aircraft to remove them.
We did it with Kuwait and Iraq in 90/91 and we did it in Beruit/Lebanon in what, 08? Where the folks were at the airport but couldn't get out, so they sent in the navy and Marines to helo them to ships where they were taken to another destination where they could get out.
As for personel, yes the military does have personel assigned for such a task. Some are key civilians who would not be evacuated or be one of the last to go. I recently applied for such a position oversees where that was part of the duties, to coordinate with the dependants and the comand.
Lets not forget that bases have the base personel and what we call "tenants" The base personel are assigned to the base, these are your cooks for the main mess hall, the MPs assigened to the base, the electricians and construction personel who conduct daily maintenance, the com. and weather and MWR personel, initialy all of these folks would remain at their base since they would not belong to the units going into action.
And it would be these personel and the <civilian position> dependant readiness coordinator and his military oposite number an adjudant on the base comanders staff most likely who would coordinate this with the logistics side of the house at whatever port of entry/exit they would be using. At which time they would contact the base motorpool or contract with a civilian entity for transportation, a special train, a convoy of buses either military or a civilian bus line and they would be shuttled to the airport or seaport or train station where they would be embarked.
Civilians not in the DOD would be dealing with the state Department and embassy/consul, they would be given warnings, have to register, have communication assets to the point of a daily check in. And if the call comes they go or they may have part of the Marine Det come and get them, or they will be left on their own.
At which point they would be evacuated with other personel, either civilians, or even with the embassy staff via some of the methods already discussed. Usualy this will occur before things get to nasty, we have been kinda sensitive since Iran. And alot of our embassys now are what we call "turn key" meaning they are open and closed like a regular buisness and no staff remain on the grounds other than local guards.
Other citizens who are not part of DOD, would most likely be left in the hands of the State Dept and the Red Cross and a few attempts would be made to extricate them, either meet at Airfeild X and a C-130 or Helos will pick you and everyone else up, or to the city Y and a ship will pick you up and again take you to a safe place. Others will be instructed to go to the train station and go to the nearest nuetral country where they will then make their way home. And some will be told "YOU WERE WARNED! YOU DID NOT LISTEN! !!! GOOD LUCK! YOUR ON YOUR OWN!"