All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
There is no doubt that if the person praying behind an imam delayed rising from thr prostration until the imam started reciting Al-Faatihah, this is considered contrary to the Sunnah, because the Sunnah is that one performs the Rukn of the prayer immediately after the imam without delay and that he performs the acts of the prayer immediately after the imam performs them.
Anas, may Allah be pleased with him, narrated that the Prophet said, “The imam is appointed to be followed: so when he says the Takbeer, say the Takbeer; when he bows down for Rukoo‘ (the bowing), bow down for Rukoo‘; when he stands up from the Rukoo‘, stand up from it; when he says: Sami‘ Allahu liman hamidah (Allah listens to him who praises Him), say: Rabanna lak-al-hamd (Our Lord, to you is Praise); and when he performs the Sujood (prostration), perform Sujood.” [Al-Bukhaari and Muslim]
Also, Al-Baraa’, may Allah be pleased with him, narrated, “When the Prophet said, Sami‘ Allahu liman hamidah, none of us bent his back (for Sujood) till the Prophet prostrated, and then we would prostrate after him.” [Al-Bukhari and Muslim]
Al-‘Ayni said:
“The meaning of the hadith is that the person led in prayer starts after the imam has started the pillar and before he finishes it, so that following (of the Imam) would be achieved. Also, the hadith of ‘Amr ibn Saleem, narrated by Muslim, reads, ‘No one would bend his back [to go down for Sujood] until he [the Prophet] was completely in the Sujood position.’ Also, Abu Ya'la narrated from the hadith of Anas, ‘...until the Prophet was in complete Sujood.’ The meaning of all of this is clear, that the person led in prayer begins the pillar after the imam has started performing it and before he finishes it.”
Besides, the Shaafi’i book Haashiyat Al-Jamal reads, “The desired following (of the imam) is achieved when the one praying behind him does not start performing the act of prayer until the imam has started performing it, and the imam finishes performing that act before the one praying behind him finishes it. What is even more perfect in this regard is that the one praying behind him does not start performing the act of prayer until the imam has completely moved to the new position in prayer...”
However, the delay that is contrary to the Sunnah which you mentioned in the question does not result in invalidating the prayer, as long as the one praying behind the imam catches up with the imam in the standing position before he bows down for Rukoo‘. The scholars of Fiqh call this a delay within the Rukn.
Shaykh Ibn ‘Uthaymeen said:
“The delay within the Rukn means that you delay in following the imam but you catch up with him in the Rukn which he moved to, like when the imam bows down for Rukoo‘ and you have one verse or two verses from the surah left, and you remained standing to complete the surah, but you bowed down and caught up with the imam while he was in Rukoo‘, so the unit of prayer is valid here, but the action is contrary to the Sunnah because what is legislated is that you start the Rukoo‘ right after the imam has reached Rukoo‘ and you do not delay from it.”
For more benefit, please refer to fatwas 16498 and 183337.
Allah knows best.