I only play coin games and 3 hole games against a friend, who I know personally, yet I tiered up from master to tour master a few weeks ago. So I am assuming the coin games do count on mobile ?
Everything counts on mobile, because each game contributes to the XPs and levels.
Your experience underlines what I heard: Tiers on mobile are connected to levels, and up to Tour Master. While H2H and other mobile games are practice by definition and don't count towards the average, you have been promoted in tier by levelling up.
But, if you want to become Legend, you have to play ranked strokeplay for a 61.00 average.