Loud Zikr after fardh or sunnah prayer
In the name of Allah, the most Beneficent, the most Merciful.
Saaiduna Abdullah Ibn Abbas Radiallahu Anhu narrates that the raising of the voice of the zikr was practiced in the time of the Prophet of Allah Sallallahu Alahi Wasalam when they left the obligatory prayer. And Ibn Abbas Radiallahu Anhu said “I would know of when people left the obligatory prayer by the (loud) zikr and I used to hear it.” (Sunan Abi Dawud p.150 v.1)
From the above narration we can establish that it is permissible to recite the various forms of zikr, tasbih and dua after the fardh prayers.
Allahmah Ibn Abideen Shami (RA) states in his Raddul Muhtar that raising ones voice whilst doing zikr is permissible except when one disturbs a sleeping person, the one engaged in prayer and the one reciting Quran. (Raddul Muhtar p.434 v.2)
Therefore, with regards to your question, if the Muazzin reminds people by reading the various Tasbeeh and Durud Shareef loudly then there is nothing wrong as long as it is not considered a sunnah and that those who do not wish to join are not condemned.
Only Allah Knows Best
Mohammed Tosir Miah
Darul Ifta Birmingham.