So like Lenin's decision on Petrograd and Moscow, the federal government concludes that it should move away from the South in the case of another kinetic war? Interesting.
From the Constitution Article 1 Section 8, "The Congress shall have Power ... To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of Particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards and other needful Buildings;" So it is in PA's power to carve out from itself a small section, on either side of the Schuylkill River, for the use of Congress. This move in seat of government, as you said, is done as a matter of security. Between the Revolution, 1812, and the Civil War, many constructions were provided for the defense of Philadelphia and the Delaware River Basin, so Phillie certainly fits the bill.
For your question, I imagine that Congress would have to kindly negotiate over the particular section ceded, so that Pennsylvania and PA-Philadelphia retain their shipyards and docks, factories, or whatever they had in the 1860s. The PA government can in theory cede the entire city, but may not feel inclined to do so. They do have their own economic interests in retaining the bulk of it.
Decades and centuries down the line, the areas surrounding this new District of Columbia (Franklin, D.C.?) do stand to gain from the growth of the federal government and its employees' needs, much as Maryland and NOVA did.
I always thought it would be amusing if an independent CSA simply re-receded Alexandria/Arlington as a federal district: to remove it from the heart of Virginia and wisely prevent the growth of any "first state among equals" notion in a country that already had a hard time with member states pushing back against President Davis in Richmond, but also to plant it a stone's throw from Washington D.C. just to be dicks about it.
