ANSWER:

As long as you and the imam were in the ruku position together even for a few seconds, the rakat is valid. But if you are not certain, you must add another rakah after the salam.

Is my rakat valid if the imam goes to rukoo while I still have a few words to say in fatiha, then I go down to rukoo and maybe 1-2 seconds later the imam says “Sami’ Allah…”. I still say the tasbeeh and then stand up before he goes for sujood