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.
The statement that you mentioned is correct and in conformity with what was determined by the majority of the scholars; that the Takbeer is said during the transition (i.e. when moving down from the standing position to the Rukoo’ [bowing] position). Please, refer to fatwa 120581.
Therefore, if you raise your hands while still standing and before bowing down, then you should not say the Takbeer until you start moving down to the Rukoo’, and if you say the Takbeer while standing or you started saying the Takbeer while standing, then you did not comply with the Sunnah.
According to the scholars who say that it is an obligation to say the Takbeer, such as the Hanbalis, your Takbeer is not sufficient because you say some of it before the transition, and if some of the Takbeer is said before the transition or after it, then this is not sufficient according to them. The Hanbali book Ar-Rawdh reads, “If he (a praying person) starts the Takbeer before moving (to the Rukoo’) or he completes the Takbeer after it (after moving down to Rukoo’), then this is not sufficient (i.e. it is as if he did not make the Takbeer).”
However, according to the scholars who hold that the Takbeer is an act of the Sunnah (not an obligation), which is actually the view of the majority of the scholars, then your prayer is valid but you did not conform to the Sunnah in this respect.
Allaah knows best.