ACR X TCASII TA WITH MIL JET SPILLOUT FROM R-4008 HAD LTSS. EVASIVE ACTION TAKEN.

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ACR X CRUISING AT FL330 ABOUT TO FLY OVER PXT VOR WHEN ZDC CLRED US TO DSND TO FL240. AS THE CAPT BEGAN DSNDING; OUR TCASII ISSUED A TA AND TCASII SHOWED AN ACFT 1200 FT BELOW AT 2 O'CLOCK FROM OUR POS AND CLBING. THE CAPT DECIDED TO STOP THE DSCNT AND WE STARTED LOOKING FOR TFC. WE SIGHTED ACFT IN A HARD L TURN ALREADY TO OUR 10 O'CLOCK POS. A MIL JET; WE LATER FOUND OUT; HAD 'SPILLED OUT' FROM A RESTR AREA AND WE ALSO FOUND OUT THAT THAT WAS NOT THE FIRST TIME THIS HAS HAPPENED IN THIS AREA. IT SEEMS THAT THE RESTR AREA IS NOT SUFFICIENTLY LARGE TO CONTAIN THE MANEUVERS AND ACFT OF SUCH HIGH PERFORMANCE. THE AREA IS R-4006 AND SITS BTWN J-191 AND J-79; 2 MAJOR AIRWAYS CARRYING A LOT OF AIRPLANES WITH LOTS OF LIVES. SUPPLEMENTAL INFO FROM ACN 294949: I STARTED THE DSCNT WE RECEIVED A TCASII ALERT. IT SHOWED TFC AT 12 O'CLOCK; 1200 FT BELOW US; CONVERGING AND CLBING. I IMMEDIATELY LEVELED OFF AT FL325. TFC WAS STILL CLOSING. I THEN INITIATED A CLB BACK TO FL330 AND ASKED ZDC IF THEY HAD ANY CONFLICTING TFC. ATC'S RESPONSE WAS 'NEGATIVE.' AT ABOUT THIS TIME; WE MADE VISUAL CONTACT WITH AN ORANGE TWIN TAILED FIGHTER; JUST AHEAD AND BELOW US; IN A HARD L TURN. THE ACFT CAME WITHIN 1 MI AND 1000 FT AS IT PASSED OFF TO OUR L. IF WE HAD NOT RECEIVED THE TCASII ALERT AND TAKEN EVASIVE ACTION; IT WOULD HAVE BEEN A LOT CLOSER. WE NOTIFIED THE CTLR THAT WE WOULD BE FILING A NEAR MISS RPT. I SPOKE WITH THE WATCH SUPVR. HE STATED THAT THE OTHER ACFT WAS A 'SPILLOUT' FROM R-4008 AND UNDER CTL OF 'PXT CTL.'