The current rulebook in the Force Awakens core set completely removed the old "Imperial player has Initiative on a tie" rule.
The current sample game never mentions Initiative and doesn't need it (there are no obstacles and no tied Pilot Skill values), and both the learn-to-play booklet and the full rules reference have only one rule now: cheaper list chooses which player has initiative, or a random player chooses on a tie. This is for all games now, not just tournaments.
Some missions always give a certain side Initiative, but they're special.
Playing casually, in the case of a tie for squad cost, we roll an attack die ... whoever rolls higher (Critical > Hit > Focus > Blank) chooses which player has initiative.