Sheikh, We have been brought up with teaching that Imam is our leader, who takes burden of our prayers in court of Allah. So respect for the Imam has always been cornerstone of my Iman. We are in a small musallah where we have a designated Imam. Elhamdulilleh he is a good Imam. Sometime he is a few minutes late here and there, but we have never seen him disrespect any one or shout or anything. Most of our masjid wait for imam so we can pray together and he always appreciates this.
I was very shocked the other day when our masjid administrator attended the zuhr and Imam was 2-4 minutes late. The admin stood up and performed Imamat. After salah, admin took the imam to back room and we could hear him scolding the Imam.
As a regular person I did not intervene, but my heart is shattered. How can the admin, who is just a servant of community disrespect our Imam. The admin does not even come regularly. I cannot respect him just because he has money and fancy car. He shouted at my Imam. My heart is broken having witnessed this. I feel my zuhr salah is not valid behind the admin. Should I repeat it?
Assalāmu ʿalaykum waraḥmatullāhī wabrakātuh,
At the outset, we admire and appreciate your love and respect for the Shiʿār of Islām. It is indeed a sign of Īmān. We would also point out before anything else, that the Imām in question is incorrect in his punctuality. We live in a time where-in punctuality drives regular life. A congregation is expected to be completed by a certain time so that the congregants can return to their regular life, work and appointments. Hence, the Imām should definitely work on his punctuality and keep the comfort of people in mind.
What is interesting to note is that the congregants do not seem to mind an occasional delay from the Imām while the organizer has an issue with it. To understand the sharʿī boundaries for this interaction, it should be kept in mind that the Imām has entered into a contract to make himself available for the specific times. His wagers are in lieu of the time and not some particular worship(s). This entails that being late for presenting himself for his job is indeed an infractionable offense. The Imām should know this and should make sure that he is present a few minutes prior to the congregation. If a review of his absenteeism, purely from the contractual stance is taken and he is penalized or terminated for continuous disregard for the punctuality, it will not be against sharīʿah.
Having said that, we also take note that the congregants do not have any problem with him. So, should for some reason a designated Imām is delayed, then sharʿan it is still the Imām’s right to lead the congregation. ʿAllāma al-Ḥaskafī raḥimahullah has mentioned,
“…(and) know that (owner of the house) and the like and the designated Imām of the masjid (is more worthy to lead the salāh than anyone else) generally… ”
ʿAllamah ibn al-Abidīn raḥimahullah explains further that “…even though there may be a more knowledgeable, and better recited within the congregation…” 
When termination of an Imām is concerned, despite in our contemporary construct of the contractual agreement, even when the Imām is transgressive in religion, it may still be disliked terminating him from position, lest it creates further discord and fitna in community. In such a case, it is much more acceptable that he be given due course of counseling to help him reform from his lapses. 
Then, the issue arrives at the trustee’s handling of the situation. The action of the trustee does not only belittle the entire field of wisdom, but also shows that the individual has no clue how to handle crisis in a worship place. Masājid are places where the faith of congregants is cultivated and nurtured. At its core, Imām forms the source for this nurturing. To disrespect, ridicule and belittle the Imām in the way described in the question is unquestionably un-islamic, worthy of rebuke and reprimand.
No individual deserves to be ridiculed in this manner, let alone an Imām of a Masjid in presence of his congregants. Rectification requires precision, forbearance and wisdom. The trustee shows lack of all these qualities. Such individuals are inept for the position of administration they flaunt at every chance they find. Alas, it is starting to feel like a recurring pandemic in our communities wherein religious leaders, regardless of their stature and astuteness in dīn, are subjected to such ignorant trustees who treat masājid and like their property. The trustee is equally, if not more, deserving of rectification and iṣlāḥ and some senior should speak to him and rectify his incorrect actions so he does not transgress in future as he has done here.
Finally, your concern is with regards to the dhuhr salāh which was led by this trustee. The trustee, while transgressor in his actions and character, is still a Muslim. Salāh behind him, although Makrūh, is still valid. You do not need to repeat it. 
And Allāh Taʿālā Knows best,
Mufti Faisal al-Mahmudi
الدر المختار وحاشية ابن عابدين (رد المحتار) (1/ 559)
(و) اعلم أن (صاحب البيت) ومثله إمام المسجد الراتب (أولى بالإمامة من غيره) مطلقا
حاشية ابن عابدين (رد المحتار) (1/ 559)
(قوله مطلقا) أي وإن كان غيره من الحاضرين من هو أعلم وأقرأ منه. وفي التتارخانية: جماعة أضياف في دار نريد أن يتقدم أحدهم ينبغي أن يتقدم المالك، فإن قدم واحدا منهم لعلمه وكبره فهو أفضل، وإذا تقدم أحدهم جاز لأن الظاهر أن المالك يأذن لضيفه إكراما له. اهـ.
الدر المختار وحاشية ابن عابدين (رد المحتار) (1/ 549)
((ويكره تقليد الفاسق ويعزل به إلا لفتنة. ويجب أن يدعى له بالصلاح)) أي بالفسق لو طرأ عليه… وعند الحنفية ليست العدالة شرطا للصحة فيصح تقليد الفاسق الإمامة مع الكراهة؛ وإذا قلد عدلا ثم جار وفسق لا ينعزل؛ ولكن يستحب العزل إن لم يستلزم فتنة
الاختيار لتعليل المختار (1/ 58)
ويكره إمامة العبد (ف) والأعرابي والأعمى (ف) والفاسق
بدائع الصنائع في ترتيب الشرائع (1/ 156)
(ولنا) ما روي عن النبي – صلى الله عليه وسلم – أنه قال: «صلوا خلف من قال لا إله إلا الله» ، وقوله – صلى الله عليه وسلم – «صلوا خلف كل بر وفاجر»