When Fighting Defensively should provide the following benefit: You take only a –2 penalty on attack rolls for fighting defensively. While using this style and fighting defensively or using the total defense action, you gain an additional +1 dodge bonus to your Armor Class.
However, applying Crane Style as a Temporary Bonus is adding the +1 dodge bonus to AC even when the Fighting Defensively Temporary Bonus is not selected.
Also, it is not reducing the -4 attack penalty you normally have when fighting defensively to a -2 penalty.
I would assume these issues also apply when the Total Defense Temporary Bonus is selected.