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.
There is no doubt that the Sunnah for a person who is led in the prayer is to follow the Imaam in the movements of the prayer in a way that he does these movements immediately after the Imaam does them; for more benefit, please refer to Fatwa 85130.
As regards doing the actions of the prayer at the same time the Imaam does them, in a way that one’s Ruku’ and prostration is exactly at the time as the Imaam, then this does not invalidate one’s prayer but it is disliked and one may lose the excellence of the congregational prayer according to the view of some jurists . This is not due to disrespecting the Imaam, but because of not following the Sunnah.
Moreover, the Sunnah for the Imaam, the person who is led in prayer and the person who is praying alone is to say Allaahu Akbar (Allaah is the Greatest) when bowing down and prostrating at the time of moving, so he starts the Takbeer (saying Allaahu Akbar) at the beginning of bowing down or prostrating or standing up, and he finishes when he would have finished the movement of moving from one action to another in a way that the Takbeer lasts for the entire movement from one action to another, and he should not delay the Takbeer until he would have reached the position of bowing down, prostrating or standing up, as some Imaams do with the pretext that he does not want the people who are led in prayer to precede him in movements or do the actions at the same time when he does them.
Therefore, we advise you to teach your Muslim brothers who pray with you (both the Imaam and the people led in prayer) this Sunnah in a soft and gentle manner, because knowledge is obtained by learning, and whoever guides people to do good, he gets exactly the same reward as the one who performs that good deed without diminishing anything from their reward as confirmed in an authentic Prophetic narration.
Allaah Knows best.