What is the ruling regarding the prayer of an Imam who deliberately bows after the congregants?

The prescribed manner for the transitional takbirat (utterances of "Allahu Akbar") is for them to coincide with the movement. So, the takbir should begin when one starts to bend and conclude before reaching the bowing position, so that the takbir occurs between the states of standing and bowing. This is based on the hadith of Abu Hurayrah: "The Messenger of Allah (peace and blessings be upon him) used to say the takbir when he stood for prayer, then he would say the takbir when he bowed..."

Therefore, if the Imam pronounces the takbir for bowing before starting the bowing movement, it is an error. The error is compounded if he completes the takbir before bending. Many Hanbalis consider the prayer of one who performs part of the takbir out of its proper place invalid, as it is a breach of an obligation. If done intentionally, the prayer is invalidated. If done out of forgetfulness, sajdat as-sahw (prostration of forgetfulness) is required. However, the meticulous scholars among them hold that this is pardoned to alleviate hardship.

As for the congregants (ma'mumin), they are not permitted to bow before the Imam. Following him is obligatory, and it is impermissible to precede him or to be excessively delayed behind him, based on the Prophet's (peace and blessings be upon him) saying: "Indeed, the Imam is appointed to be followed. So when he says the takbir, say the takbir; and when he bows, bow..." and his saying: "...So do not precede me in bowing..." Some scholars have explicitly stated the prohibition of preceding the Imam, and that intentionally doing so may invalidate the prayer.

In summary: The Imam must begin the takbir simultaneously with initiating the transition, and the congregants must follow the Imam in all actions of the prayer without preceding him.