Out of Play

I think it depends on which network is carrying the game.

OBR 5.10 The ball becomes dead...

(f) When a fielder, after catching a fly ball, falls into a bench or stand, or falls across ropes into a crowd when spectators are on the field. As per runners, the provisions of 7.04 (c) shall prevail. If a fielder after making a catch steps into a bench, but does not fall, the ball is in play and runners may advance at their own peril.

7.04 (c)...If the fielder or catcher, after having made a legal catch, should fall into a stand or among spectators or in the dugout after making a legal catch, the ball is dead and runners advance one base without liability to be put out.