Is there an action window to trigger abilities once the point limit has been reached?
It's not actually completely simultaneous; the Runner wins the game.

From the Android: Netrunner FAQ:


  If the Runner steals an agenda from Jinteki using the core set identity, but has no cards in hand, who wins?
  The Runner wins the
  game. Whenever a player has 7 or more  agenda points in his score
  area, the game immediately ends. The  game ending takes precedence
  over any conditional ability that  triggers when an agenda is stolen.