In what zone do the lingering effects of spells reside?
They do not reside in any special realm. They just continue to apply. CR 611.2a states


  A continuous effect generated by the resolution of a spell or ability lasts as long as stated by
  the spell or ability creating it (such as “until end of turn”). If no duration is stated, it lasts until
  the end of the game.


What is interesting is, that these effects continue to apply even if the controller of the spell or ability that generated it leaves the game in a multi-player. So, if you turned some of your opponent's lands into swamps and then are killed, those lands continue to be swamps as long as they remain on the battlefield with the counters. Since you already left the game, your turn will be skipped and no counters are removed by the tomb's second ability.