All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If it is verified that the statement of a Companion contradicts the saying of the Prophet then, in this case, it is an obligation to do the following two things:
1- First: to act in accordance with the saying of the Prophet and leave the statement of whoever contradicted him even if it is a Companion. This is because in Islam, we are commanded to follow the Prophet who conveyed to us the message of his Lord and was infallible. Conversely, others are not infallible, even Companions. Imam Ash-Shaafi'i said: “[Scholars) agree that once a Sunnah of the Prophet becomes evident to someone, it is not permissible for him to leave it and act in accordance with the statement of any person, regardless of who it is.”
Ibn Taymiyyah said: “It is an obligation to follow the statements, commands and prohibitions provided in the Quran and the Sunnah and no consideration should be given to anyone who opposes those, whoever that person may be. And it is not permissible to follow anyone in opposition to that, whoever it is. This is because the Quran and Sunnah and the consensus of Muslim scholars indicate that we are to follow and obey the Prophet .”
Ibn Al-Qayyim said in I’laam Al-Muwaqqi'een: “Whoever studies the biography of the Companions will notice that they never left a Sunnah and followed a statement of anyone else, no matter who it was. Ibn ‘Umar used to leave the statement of ‘Umar (his father) when the Sunnah became evident to him, and Ibn ‘Abbaas used to censure those who opposed a Sunnah that they heard and cited what Abu Bakr and Umar said as evidence. He would say to them: 'Stones are about to descend upon you from the heaven, I tell you: the Prophet said, and you tell me: Abu Bakr and ‘Umar said?!'”
On the other hand, the statement or action of a Companion that opposes the Sunnah does not abrogate something that has been verified that the Prophet said or did, because the action alone is not evidence that the Companion did it for the purpose of abrogating. He might have forgotten, or he might not have had knowledge about that Sunnah of the Prophet . We cannot say that something is abrogated unless there is certain evidence. Ibn Al-Qayyim said: “It is an obligation to follow the Sunnah of the Prophet and judge by it unless there is certain evidence that something from it was abrogated or that the Muslims as a whole agree to act in contrast to something from it, the latter of which is impossible; as, thanks to Allaah, the Muslims have never agreed to abandon a single Sunnah, except a Sunnah that is known to be abrogated and the Muslims knew that it was abrogated. In that case, it is an obligation to act according to the new judgment which abrogated the previous judgment. As for leaving the Sunan for a statement of any person, it is not permissible, regardless of who it is.”
2- Second: It is an obligation to think good of the Companions and to find excuses for them, as the Companions are known to be the most enthusiastic people in following the Sunnah and the most obedient to Allaah and His Prophet . If any of them said or did something that goes against the Sunnah of the Prophet then there is no doubt that he has an excuse. He may not have known what the statement of the Prophet said or he may have forgotten or misinterpreted it, or some other excuse.
As for some Companions praying Sunnah prayers after the Iqaamah, as you mention, Ibn Qudaamah said in Al-Mughni about this very issue after citing some Companions on the permissibility of beginning a Sunnah prayer after the Iqaamah: "Our evidence is that the Prophet said: “If the obligatory prayer is called, there is no prayer except the obligatory prayer.” [Muslim] Ibn ‘Abdul-Barr said with regard to this issue: “When there is disagreement, judgment goes to the Sunnah, so whoever puts forth the Sunnah as evidence shall prosper, and whoever practices it shall be saved.”
Ibn Hajar said in Al-Fat-h: “Ibn ‘Abdul-Barr and others said that when there is disagreement, judgment must go to the Sunnah, so whoever puts forth the Sunnah as evidence shall prosper. Leaving the Sunnah prayers when the Iqaamah is called and then performing it after having completed the obligatory prayer is nearer to the Sunnah. This is also supported by the fact that in the Iqaamah one says ‘Come to the prayer’ - that is, come to the prayer whose Iqaamah is being called. So the best situation is to act in accordance with this command rather than do something else, and Allaah knows best.”
Based on the above, you should know that it is not permissible to initiate a Sunnah prayer after the Iqaamah, and whoever did it among the Companions, it is either because he did not know what the Prophet said or because he believed that the judgment applies to someone who would miss prayer with the Imaam, or he had some other excuse.
For more benefit on the reasons why the Companions differed, please refer to Fatwa 84153. Refer also to Fatwa 85732 for information about everyone being prone to mistakes except the Prophet . Finally, refer to Fatwa 220702 about the view of Abu Haneefah regarding praying two Rak'ahs of Sunnah of Fajr if one is sure that he will not miss the congregational prayer.
Allaah Knows best.