Du`a' is an act of worship. Acts of worship are Tawqifiyyah (bound by a religious text and not amenable to personal opinion). Therefore, it is not permissible to say that an act of worship is prescribed - with regard to its principle, number, form, or place except with proper Shar`y (Islamically lawful) evidence. We do not know of any Sunnah concerning that which was narrated from the Prophet (peace be upon him), whether in word or deed, or his approval, which would point to the claim made by the second group. All goodness is in following the guidance of the Prophet (peace be upon him). Furthermore, the acts he (peace be upon him) used to do after prayer are known by the well-grounded proofs. As are the acts of his Caliphs, Companions, the followers, and those who followed them in goodness. Whoever introduces anything that goes against the guidance of the Messenger (peace be upon him) will have it rejected. The Prophet (peace be upon him) said:
Whoever does an action which is not in accordance with this matter of ours (Islam), will have it rejected.
The Imam who recites Du`a' after saying Taslim (salutation of peace ending the Prayer) (Part No. 7; Page No. 99) while the Ma'mums (persons being led by an Imam in Prayer) say 'Amin', all of them raising their hands, should be asked for evidence to support his action, otherwise it is to be rejected. The same applies to a person who does that after supererogatory prayers; he should be asked for evidence as Allah says:
Say (O Muhammad صلى الله عليه وسلم), "Produce your proof if you are truthful."
We do not know of any evidence from the Qur’an or Sunnah which suggests that what the second group claims is prescribed in Islam, namely, reciting Du`a’ collectively and reciting Dhikr in the manner mentioned in the question.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.