From the ATP rulebook on MC elimination rules - it seems kind of cumbersome, so I didn't bother to read it all, but I think it may answer your question (in D(3)c subsection e.g. ?)
III. WORLD CHAMPIONSHIPS
3.01 TENNIS MASTERS CUP
B(4)(c) The Alternate(s) is eligible to play in the Single Elimination competition and to receive points and prize money if he qualifies.
D. Order of Play - Round Robin
3) The final standings of each group shall be determined by the first of the following methods that apply:
a) Greatest number of wins;
b) Greatest number of matches played;
c) Head-to-head results if only two (2) players are tied,
or if three (3) players are tied,then:
i) If three (3) players each have one win, a player having played less than all three (3) matches is automatically eliminated and the player advancing to the Single Elimination competition is the winner of the match-up of the two (2) players tied with 1-2 records; or
ii) Highest percentage of sets won; or
iii) Highest percentage of games won.
iv) If (i), (ii) or (iii) produce one superior player (first place), or one inferior player (third place), and the two remaining players are tied, the tie between those two players shall be broken by head-to-head record.
4) If ties still exist after the above procedures, the Steering Committee shall make the final determination.
5) In applying the tie-breaking procedures, a conduct default or retirement shall count as a straight-set win or loss. However, games won or lost in matches with the defaulting or retiring player shall not be counted in the application of subsection 3.c. (iii) above. A player who retires during the Round Robin because of illness or injury may continue in the competition if it is approved by the Tournament Doctor.
E. Single Elimination Competition
1) The winner of each group shall be placed in separate semifinal brackets. The runnerup of each group shall be placed in the semifinal bracket with the winner of the opposite group.
I thought this part was interesting - no wonder they all show at the media conference! Curious if anyone has ever been fined this 5%?
"2) All Direct Acceptances and the Alternate must appear at the site of the event(s) as determined by the ATP and participate in the pre-tournament media conference. Failure to appear shall result in a penalty of five percent (5%) of total ATP prize money earned during the ATP circuit year.