`Umar ibn Al-Kattab (may Allah be pleased with him) never violated the teachings of the Prophet (peace and blessing be upon him). As for the point your referred to in your question, there are many other proofs that indicate that the Prophet (peace and blessings be upon him) regarded triple divorce as three divorces.

The eminent Muslim scholar Sheikh `Abdel Khaliq Hasan Ash-Shareef, the renowned da`iyah, states:
“As for the issue of triple divorce and `Umar ibn Al-Kattab’s ijtihad (personal reasoning) on it, consider the
following points:

1. According to the hadith you referred to, the Prophet (peace and blessings be upon him) became angry when he was told that a man had pronounced three divorces at one time. Did you ask yourself why the Prophet (peace and blessings be upon him) got angry at that action? The man who divorced his wife three times at once violated the teachings of the Qur’anic verse: “Divorce must be pronounced twice and then (a woman) must be retained in honor or released in kindness” (Al-Baqarah: 229). This Qur’anic verse guides Muslims that divorce should be two separate times, and then if the spouses cannot live together, the last divorce could be pronounced. Therefore, the person who pronounced three divorces at once violated the guidance of this Qur’anic verse.

2. There are other proofs that maintain that the Prophet (peace and blessings be upon him) regarded the triple divorce as three divorces. In his Zad Al-Mi`ad, Ibn Al-Qayyim states about 22 proofs to that effect. Also, this is the opinion of many of the Prophet’s Companions, the majority of the successors, and the imams of the four schools of fiqh (Islamic Jurisprudence).

3. The Prophet (peace and blessings be upon him) ordered us to follow the guidance of the Rightly-Guided Caliphs, saying, “Follow my Sunnah, and that of the Rightly-Guided Caliphs after me.”

4. What `Umar ibn Al-Khattab did was meant to preserve the community and protect it. He, as the Caliph of the Believers, had the authority to do that. There is a golden maxim in fiqh that says that the command of the imam puts an end to ikhtilaf (disagreement among scholars). In Arabic this is “amr al-imam yarfa` al-khilaf.” Sometimes, the Muslim community would be in need of resolving the ikhtilaf over a given issue; otherwise dissension and disorder may creep into the society. The main responsibility to resolve ikhtilaf falls on the shoulders of the community leaders and those in charge of the people affairs.”