Does the formula of divorce, suspended on a past action, take effect, such as saying: "If you did such and such, then you are divorced"?

What you uttered is considered a divorce, not a threat or an oath. It is a contingent divorce, contingent upon a factual occurrence, and thus considered an accomplished divorce. If this was the first or second divorce, you can take your wife back as long as her waiting period ('iddah) has not ended. If her waiting period ends before you take her back, it becomes a minor irrevocable divorce (baynunah sughra), and you can remarry her with her consent and the consent of her guardian (wali). However, if this was the third divorce, it has become a major irrevocable divorce (baynunah kubra), and she is not lawful for you until she marries another man in a valid marriage and he consummates it with her.