The rules clearly cover what should happen when a play is blown dead, but do not clearly cover what should happen when this is done incorrectly. Following are the rules for what should happen when a play is blown dead correctly.
Quotations come from the MLB rulebook for 2015.
Once an umpire calls "time", the ball is dead:
5.12 Calling “Time” and Dead Balls
(a) (3.12) When an umpire suspends play, he shall call “Time.” At
the umpire-in-chief’s call of “Play,” the suspension is lifted and
play resumes. Between the call of “Time” and the call of
“Play” the ball is dead.
Once a ball is dead:
(5.09) The ball becomes dead and runners advance one base, or
return to their bases, without liability to be put out, when:
(1) A pitched ball touches a batter, or his clothing,
while in his legal batting position; runners, if
(2) The plate umpire interferes with the catcher’s
throw attempting to prevent a stolen base or retire
a runner on a pick-off play; runners may not
(5.02) While the ball is dead no player may be put out, no bases
may be run and no runs may be scored, except that runners may
advance one or more bases as the result of acts which occurred
while the ball was alive (such as, but not limited to a balk, an overthrow,
interference, or a home run or other fair ball hit out of the
Rule 5.06(c)(2) Comment (Rule 5.09(b) Comment): Umpire
interference may also occur when an umpire interferes with a
catcher returning the ball to the pitcher.
(3) A balk is committed; runners advance; (See Penalty
6.02(a) (Penalty 8.05).)
(4) A ball is illegally batted; runners return;
(5) A foul ball is not caught, in which case runners
return to their bases. The umpire-in-chief shall not
put the ball in play until all runners have
retouched their bases;
(6) A fair ball touches a runner or an umpire on fair
territory before it touches an infielder including
the pitcher, or touches an umpire before it has
passed an infielder other than the pitcher; runners
advance, if forced.
If a fair ball goes through, or by, an infielder, no
other infielder has a chance to make a play on the
ball and the ball touches a runner immediately
behind the infielder that the ball went through, or
by, the ball is in play and the umpire shall not
declare the runner out. If a fair ball touches a runner
after being deflected by an infielder, the ball is in
play and the umpire shall not declare the runner out;
Rule 5.06(c)(6) Comment (Rule 5.09( f ) Comment): If a fair
ball touches an umpire working in the infield after it has
bounded past, or over, the pitcher, it is a dead ball. If a batted
ball is deflected by a fielder in fair territory and hits a runner or
an umpire while still in flight and then caught by an infielder it
shall not be a catch, but the ball shall remain in play.
(7) A pitched ball lodges in the umpire’s or catcher’s
mask or paraphernalia, and remains out of play,
runners advance one base;
Rule 5.06(c)(7) Comment (Rule 5.09(g) Comment): If a foul
tip hits the umpire and is caught by a fielder on the rebound,
the ball is “dead” and the batsman cannot be called out. The
same shall apply where such foul tip lodges in the umpire’s
mask or other paraphernalia.
If a third strike (not a foul tip) passes the catcher and hits an
umpire, the ball is in play. If such ball rebounds and is caught by a fielder before it touches the ground, the batsman is not
out on such a catch, but the ball remains in play and the batsman
may be retired at first base, or touched with the ball for
If a pitched ball lodges in the umpire’s or catcher’s mask or
paraphernalia, and remains out of play, on the third strike or
fourth ball, then the batter is entitled to first base and all runners
advance one base. If the count on the batter is less than
three balls, runners advance one base.
(8) Any legal pitch touches a runner trying to score; runners
Other situations not covered in this, including the situation named above, would be resolved by the umpires at their discretion. They would need to determine what should have happened on the play had they not called time. In this sense, baseball is different from other sports - many other sports simply stop action when time is called/the whistle is blown/etc., and do not permit any rectification (or only very limited rectification). Baseball attempts to "get it right" when a mistake prevents the correct outcome from occurring.