Firstly, it is not obligatory for the follower (Ma’mum) to recite behind the Imam according to our school of thought under any circumstances.
Secondly, if the situation is as you described, it is preferable for you to listen to the Surah being recited by the Imam rather than reciting by yourself when you catch up with the Imam while he is reciting. However, if you have already started reciting and the Imam goes into the Rukoo (bowing), it is better for you to continue following him rather than completing the recitation of Al-Fatiha, because following the Imam is obligatory while personal recitation is recommended. Therefore, what is stronger takes precedence over what is weaker.
And Allah knows best.
Fatwa by Dr. Khālid Naṣr