Baseball - player ejected while the ball is still "live"

Referencing this video.

Strasburg, the pitcher, was thrown out before the play had completed. He threw the ball, it went behind the batter, and the home plate umpire ejected him. But, say there had been a possible play at the plate, and Strasburg had covered home and tagged the runner out. Could that have been possible since he had already been ejected?

I would have thought the umpire should have waited until the ball was dead before ejecting the pitcher. Am I wrong?

Official Baseball Rules, rule 9.01(d):

“If an umpire disqualifies a player while a play is in progress, the disqualification shall not take effect until no further action is possible in that play.”