Fielder Runs Out of Play After Catch

 
With one out and a runner on first base (R1) and third base (R3), the batter hits a high foul pop-up behind first base. The first baseman makes a running catch in foul territory and his momentum takes him from foul territory several steps into dead ball territory. This dead ball territory is an area that the coaches and umpires had agreed was out of play during their pre-game plate conference.
 
After the first baseman enters dead ball territory with the ball, he see that R3 is tagging up and attempting to score. The first baseman returns to live ball territory (in foul ground), throws home, and R3 is tagged out. R1 remained at first base the entire time.
 
Any other action required from the umpires on this inning-ending double play?
 
Call
In NF, when a player unintentionally carries a live ball out of play, the ball is immediately dead. Each runner is then awarded one base from his base at the time of the pitch.
 
In the situation below, the batter is out since his foul pop up was caught by the first baseman. The ball became dead when the first baseman went into dead ball territory, so R3 is awarded home and R1 is awarded 2nd base.
 
Remember that both R3 and R1 must properly run the bases or be subject to being called out upon proper appeal by the defense. In other words, both R3 and R1 must properly tag-up or be at risk of an appeal.