During the first two rounds of a PGA Tour event (or on any major tour, like the LPGA Tour or European Tour), players are grouped together by random draw.
For the final two rounds of a tournament, however, players are grouped together based on their score through the prior round. The players with two (or three) best scores go in the final group, then working backward toward the worst scores to survive the cut. However, within an individual group for the third and fourth rounds, who gets to hit the first tee shot to start the round in the order of play?
According to the PGA Tour's policies, the playing order for players in groups made for the third and fourth rounds of a tournament is determined based on their score. The player with the worst aggregate score through the prior round actually goes first on the first tee, giving them the honors to start the round. The player with the best aggregate score through the prior round goes last.
Under the PGA Tour rules, a tournament director can change that order, giving honors to the player with the better score.
In the case in which both (or all three) players are tied through the prior round, then the PGA Tour's "first in, last out" rule applies. The player who gets into the clubhouse first with an aggregate score is considered the player who gets the latest available tee time and the "best score" for the purpose of honors.
This is the typical order of operations for PGA Tour events.