In response to several questions your pooler has received, the gentleman who essentially became a press wrangler at the end of the Roosevelt Room pool spray was Keith Schiller, the president's former private security chief. He now is deputy assistant to the president and director of Oval Office operations.
The president had concluded his prepared remarks and given the verbal "thank you" cue for the pool to exit. As poolers shouted questions at President Trump, who mostly looked away from the shouting reporters and ignored them, Schiller moved into a position just over your pooler's right shoulder. He loudly thanked the pool several times and directed them to exit the room through the door behind us.
Your pooler asked the White House to explain this. A White House spokeswoman replied this way via email: "The staff asked the press to leave the room. I am not going to comment any further." She has yet to respond to another inquiry about whether Mr. Schiller acted on his own, or if he was asked to help the wrangler usher the press from the Roosevelt Room.