I "think" the first tie breaker is if he's offered the same max deal by his former franchise, and he was there for 5+ seasons. Then the pitching coach, then the bullpen coach, then ball park factors.
If the oppossing team doesn't have a pitching coach yet, I'm not sure if it defaults to their PC last year, or down to the next tie breaker, or perhaps to the top PC available. Either way, in a case like that, I don't think the guy will sign until all coaches are hired (ie on the last day of FA prior to the Rule 5 break at approx 3:00 est or whenever your league sims at that time frame)