Crane Clan ability when they tie, but another faction would win
The ability is definitely poorly worded. When you are tied you win refers to tie breaking, so while you would win the tie, that does not guarantee you the province win. The ability is meant to override the standard defender wins ties rules, making it easier for crane clan to win on attacks by simply tying the defense. The tie must be a tie for the win to win the province.

See discussion on BoardGameGeek.