I take it to be from the PDGA since I'm following
Competition Manual 1.9...
A. Between rounds when the groups are being reset, tied positions shall be broken. The player with the lowest score in the most recent round shall have the highest ranking when the scorecards/positions are reset. In the event of ties for lowest score across all previous rounds, the ties shall be broken by the Tournament Director through a consistently applied manner such as lowest PDGA number or alphabetical by last name.
A playoff round, be it sudden death or aggregate, is a new round of play for the participants. So the players should be ordered in the same manner that they would for any other new round of a tournament.
I suppose if it came down to the last part of the rule because the players tied in each round, a coin toss could be a consistently applied manner of tiebreaking. But I'd argue that if you're not tossing coins to break ties for the purpose of ordering players in previous rounds, then using a coin toss for the playoff wouldn't be utilizing a "consistently applied" manner in which to determine teeing order.